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Dwyer-Joyce RS Drinkwater BW and Donohoe CJ (2003) The measurement of lubricant-film thickness using ultrasound Proceedings of the Royal Society Series A Mathematical Physical and Engineering Sciences 459 (2032) pp 957-976 ISSN 1471-2946

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101098rspa20021018

The measurement of lubricant-macrlm

thickness using ultrasound

By R S Dw yer-Joyce1 B W Drinkwater2 a n d C J Donohoe12

1Department of Mechanical Engineering Mappin Street

University of Sheplusmneld Sheplusmneld S1 3JD UK2Department of Mechanical Engineering University Walk

University of Bristol Bristol BS8 1TR UK

Received 7 March 2002 accepted 13 May 2002 published online 12 February 2003

Ultrasound is reregected from a liquid layer between two solid bodies This reregectiondepends on the ultrasonic frequency the acoustic properties of the liquid and solidand the layer thickness If the wavelength is much greater than the liquid-layer thick-ness then the response is governed by the stinotness of the layer If the wavelengthand layer thickness are similar then the interaction of ultrasound with the layer iscontrolled by its resonant behaviour This stinotness governed response and resonantresponse can be used to determine the thickness of the liquid layer if the otherparameters are known

In this paper ultrasound has been developed as a method to determine the thick-ness of lubricating shylms in bearing systems An ultrasonic transducer is positionedon the outside of a bearing shell such that the wave is focused on the lubricant-shylmlayer The transducer is used to both emit and receive wide-band ultrasonic pulsesFor a particular lubricant shylm the reregected pulse is processed to give a reregection-coemacrcient spectrum The lubricant-shylm thickness is then obtained from either thelayer stinotness or the resonant frequency

The method has been validated using reguid wedges at ambient pressure between regatand curved surfaces Experiments on the elastohydrodynamic shylm formed between asliding ball and a regat surface were performed Film-thickness values in the range 50500 nm were recorded which agreed well with theoretical shylm-formation predictionsSimilar measurements have been made on the oil shylm between the balls and outerraceway of a deep-groove ball bearing

Keywords lubricant-macrlm measurement ultrasound

elastohydrodynamic lubrication macrlm-thickness measurement

1 Introduction

The durability of machine elements such as gears bearings and seals relies on theintegrity of the lubricant shylm separating the contact surfaces If the shylm fails thesesurfaces contact and friction wear and seizure can occur The thickness of an oil shylmdepends on the lubricant properties the geometry of the bearing surfaces and theoperating conditions Typically conformal contacts such as those in journal bearingsand thrust pads operate in the hydrodynamic lubrication regime with shylms of theorder of 1100 mm Counterformal contacts such as those in rolling bearings and

Proc R Soc Lond A (2003) 459 957976

957

cdeg 2003 The Royal Society

958 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

gears operate in the elastohydrodynamic (EHD) regime with shylms less than 1 mmthick The lubricant shylm should be thick enough to ensure separation of the surfacesbut not so thick that excessive pumping losses are incurred

There are many methods available for predicting the thickness of reguid shylms formedbetween surfaces based on Reynoldsrsquos equation (Hamrock 1994) These are now rou-tinely used in the design of bearing components However the measurement of lubri-cant shylms and certainly the online monitoring of shylm thickness in a component hasproved more dimacrcult

Existing techniques for lubricant-shylm measurement fall into two categories electri-cal methods and optical methods Early work (El-Sisi amp Shawki 1960) concentratedon the determination of the shylm thickness by measurement of its electrical resis-tance In later studies measurements of the shylm capacitance (Astridge amp Longshyeld1967) proved more enotective and the use of micro-transducers gave enhanced reso-lution (Hamilton amp Moore 1967) These methods require electrical isolation of thecontact elements and either give a composite shylm-thickness value over the wholebearing surface or require the positioning and alignment of small surface-mountedsensors The application of optical methods requires either that one of the contactelements is transparent or that it contains a transparent window Optical interfer-ometry (Cameron amp Gohar 1966) has proved successful in the measurement of EHDshylms and more recently boundary shylms (Johnston et al 1991) The use of lasers toreguoresce a lubricant shylm has also been used to determine shylm thickness (Richardsonamp Borman 1991) However the requirement for transparency has meant that thesemethods are rarely used outside the laboratory

In this paper a novel approach has been investigated in which the response ofa lubricant shylm to an ultrasonic pulse is used to determine the shylm thickness Themethod is such that it can be used with appropriate signal processing over a widerange of lubricant-shylm thickness Also because it is essentially non-invasive it canbe used to give online shylm measurement in real bearing components

2 Ultrasonic redegection from a layer

When ultrasound is incident on a boundary between two dinoterent media some of theenergy is reregected and some transmitted The reregection and transmission behaviourof displacement waves at the boundary is dependent on the acoustic properties ofthe two media The proportion of any incident signal reregected (or the reregectioncoemacrcient R) is given by the well-known equation

R =z1 iexcl z2

z1 + z2 (21)

where z is the acoustic impedance of the media (given by the product of density andspeed of sound) and the subscripts refer to the two media The proportion of theincident signal transmitted (or transmission coemacrcient T ) can then be calculated as

T = 1 iexcl R (22)

If ultrasound is incident on a multi-layered system then the signal transmittedor reregected is the superposition of the result of the application of (21) and (22) ateach boundary Figure 1 shows an ultrasonic beam incident on a typical lubricatedcontact which is a three-layered system consisting of steellubricantsteel The steel

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 959

ball bearing

raceway

focusedultrasonictransducer

lubricant film

I F B1 B2

Figure 1 Schematic of an ultrasonic beam incident on a lubricated contact

either side of the lubricant represents the bearing elements such as the bush andshaft in a journal bearing or the ball and raceway in a rolling-element bearing Asthe steel sections are large when compared to the wavelength of the ultrasound theycan be modelled as semi-inshynite If the lubricant layer is sumacrciently thick or theultrasonic wave packet small enough then the reregections from the top and bottombearing surfaces are discrete in time This means that if the speed of sound in thelubricant is known then the thickness of the lubricant shylm can be determined bymeasuring the time-of-regight (ToF) between the two reregections The amplitude ofthese reregected pulses can also be calculated from (21) and (22) assuming that thelosses in the lubricant are small This ToF approach is commonly used for thicknessgauging of metallic components and for corrosion monitoring As the lubricant shylmbecomes thinner the ToF approach becomes less accurate until for very thin layersthe reregected pulses overlap and it becomes impossible to distinguish the discretereregections Typically even the thickest lubricant shylms are less than 50 mm thick andso the ToF approach is rarely applicable

For a practical lubricant shylm the challenge is to extract the thickness informationfrom the reregections that are overlapping in the time domain There are a numberof approaches that can be adopted For example Tsukahara et al (1989) used thesurface waves generated by an acoustic microscope to characterize thin layers Inthis paper two alternative approaches are used Firstly the through-thickness reso-nances of the lubricant layer are measured and interpreted via a continuum modelSecondly if the lubricant-shylm thickness is so small that the frequency of the shyrstthrough-thickness resonance is above the measurable range the amplitude of thereregected signal can be measured and interpreted using a spring interface modelThese approaches are now discussed in detail

Many authors (Hosten 1991 Kinra et al 1994 Pialucha amp Cawley 1994) havedescribed continuum models of the multi-layered system response to ultrasonic wavesBased on continuity of stress and strain at each boundary in the multi-layered sys-

Proc R Soc Lond A (2003)

960 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

20 mm 15 mm

1 mm

01 mm

12

10

08

06

04

02

0 20 30 40 50 6010

f (MHz)

refl

ect

ion c

oeff

icie

nt

Figure 2 Continuum-model predictions of the redegection-coeplusmncient spectrumfrom a layer of mineral oil between two steel elements

Table 1 Acoustic properties of lubricating oil (Shell Turbo T68) at room temperature and

ambient and EHD pressures (estimated using the method of Jacobson amp Vinet (1987 ))

(Also included for comparison water and steel properties)

density bulk modulus wave velocityraquo (kg m iexcl 3) B (GPa) c (m s iexcl 1 )

oil at atmospheric pressure 876 184 1450

oil at 08 GPa 1002 126 3550

oil at 15 GPa 1044 212 4500

water at atmospheric pressure 1000 206 1483

steel 7923 172 5840

tem these models can be used to predict the reregection and transmission of planewaves through a given system Figure 2 shows a continuum-model prediction of thereregection coemacrcient spectrum for 01 10 15 and 20 mm thickness mineral oil layersbetween two steel half-spaces The material properties used in this calculation areshown in table 1 This is essentially the impulse response function of the systemie it gives the response of the system for an incident wave of unit amplitude In shyg-ure 2 the resonant frequencies are seen as sharp minima in the reregection-coemacrcientspectrum The minima seen at 363 MHz corresponds to a lubricant-shylm thicknessof 20 mm

Pialucha et al (1989) used a continuum-model approach to show that the reso-nant frequencies of an embedded layer are related to its thickness h and acousticproperties by

h =cm

2fm (23)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 961

where c is the speed of sound in the lubricant layer m is the mode number of theresonant frequency and fm is the resonant frequency (in Hz) of the mth mode It canbe seen from consideration of (23) that higher resonant frequencies correspond tothinner lubricant shylms The thinnest shylm measurable by this approach is then limitedby the upper operating frequency In practice the frequency is limited to below 4060 MHz by the attenuation of the ultrasonic pulse in the bearing materials Thismeans that if the lubricant layer is below 10 mm the resonant frequency will beabove the measurable range

The region below the shyrst resonance of a simple mass-spring system is known asthe stinotness-controlled region because the deregection of the mass is dependent purelyon the applied load and the spring stinotness In the same way it can be shown (Hosten1991) that the interaction of ultrasound with a very thin layer (which would havea very high shyrst resonant frequency) is governed by the stinotness of that layer Thestinotness per unit area K of a thin layer is given by

K =raquoc2

h (24)

where raquo is the density of the layer and c the speed of sound in the layer This springstinotness can then be used in a quasi-static model of the interaction of ultrasound withthe lubricant layer In this way Tattersall (1973) demonstrated that the reregectioncoemacrcient of the layer was given by the expression

R =z1 iexcl z2 + i(z1z2=K)

z1 + z2 + i(z1z2=K) (25)

where z1 and z2 refer to the acoustic impedance of the materials either side of thelubricant layer For identical materials either side of the lubricant shylm (z1 = z2 = z 0)this reduces to

R =1

p

1 + (K=ordmfz0) (26)

Drinkwater et al (1996) used the above analysis to determine the stinotness of drycontacts in which the interface between two rough surfaces composed of air gapsand regions of asperity contact acts like a layer of reduced stinotness Measurementof the reregection coemacrcient and hence interface stinotness can give information aboutthe degree of conformity of the contacting surfaces

Figure 3 shows a comparison between the spring-model prediction and thecontinuum-model prediction for the reregection-coemacrcient spectra from a mineral oillayer surrounded by steel It can be seen that the agreement between the two modelsat frequencies below resonance is excellent In fact within the accuracy of the com-puter the predictions are identical if f lt 1

2f1 Combining equations (24) and (26)

the thickness of the layer is related to the reregection coemacrcient by

h =raquoc2

ordmfz 0

micro

R2

1 iexcl R2

para

(27)

From (27) it can be seen that as R approaches unity so the calculated thicknessapproaches inshynity In practical measurement this means that the spring approachloses accuracy as the reregection coemacrcient approaches unity The authors have foundthat for practical purposes R lt 09 gives satisfactory results

Proc R Soc Lond A (2003)

962 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

12

10

08

06

04

02

0 10 20 30 40 50

f (MHz)

refl

ecti

on c

oeff

icie

nt

spring model

continuum model

Figure 3 Comparison between spring-model and continuum-model predictions for theredegection-coeplusmncient spectra from a mineral oil macrlm between two steel elements

3 Acoustic properties of a lubricant macrlm

To determine the thickness of a lubricant shylm using (27) it is necessary to knowboth the density of and the speed of sound through the lubricant The speed ofsound can readily be determined for oil in the bulk from a simple ToF measurementbetween a transducer and a regat reregector For the oil used in these experiments (ShellTurbo T68) the acoustic properties at 20 macrC are shown in table 1

This value is suitable for the analysis of ambient reguid wedges or low-pressurehydrodynamic lubricant shylms However in EHD shylms the lubricant is subjectedto pressures high enough to cause solidishycation and a signishycant change in physi-cal properties The speed of sound through oil under EHD conditions is thereforevery dinoterent to those in the bulk The speed of propagation of a longitudinal wavethrough a medium depends on the density raquo and the bulk modulus B accordingto (see for example Povey 1997)

c =

s

B

raquo (31)

Jacobson amp Vinet (1987) provide a model to determine the inreguence of pressureon the compression and bulk modulus of liquid lubricants They give an equation ofstate to describe the behaviour of the lubricant under pressure p

p =3B0

x2(1 iexcl x)esup2(1iexclx) (32)

and the bulk modulus under pressure is given by

B =B0

x2[2 + (sup2 iexcl 1)x iexcl sup2x2]esup2(1iexclx) (33)

where B0 is the bulk modulus at zero pressure sup2 is a lubricant-specishyc parameterand x is a function of the relative compression

x = 3

r

raquo0

raquop (34)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 963

Table 2 Details of the transducers used in this work

(The focal length and spot size (equation (55)) are determined for a centre-frequency wave inwater)

bandwidth focal length spot sizecentre frequency (iexcl6 dB points) element diameter (in water) (in water)

f (MHz) (MHz) D (mm) F (mm) df (mm)

10 417 127 76 921

25 1732 635 54 522

50 4075 635 25 121

where raquo0 is the density at zero pressure and raquop the density at pressure p These equa-tions are used for the oil both in its liquid state and after it undergoes solidishycationbut employing dinoterent values of sup2 and B0

Jacobson amp Vinet used a high-pressure chamber to measure the compression ofseveral liquid lubricants up to pressures of 22 GPa and determined the parametersfor (32) and (33) For mineral oils the bulk modulus increased from 1517 GPaat atmospheric pressure to 2030 GPa at EHD pressures while the density increasedby 2030 Therefore from (31) the speed of sound within an EHD contact is likelyto be some two to four times greater than that under ambient conditions

Unfortunately there are no test data available specishycally for the lubricant usedin these studies (Shell Turbo T68) However parameters from a similar base oil(extracted from Jacobson amp Vinet (1987)) have been used to determine the relation-ship between bulk modulus density change and pressure Table 1 shows the resultsof this analysis for two oil pressures the lower corresponding to that experienced inthe ball on regat apparatus and the higher to that in ball-bearing contact

4 Ultrasonic redegection measurement apparatus

An ultrasonic pulser-receiver (UPR) generates a high-voltage pulse that causes apiezoelectric transducer to be excited in mechanical resonance The transducer thenemits a broadband pulse of ultrasonic energy As can be seen in shygure 1 this ultra-sonic pulse propagates through the bearing shell is reregected from the lubricant layerand is received by the same transducer Measurements were made using focused ultra-sonic transducers with a range of dinoterent centre frequencies (10 25 and 50 MHz)The transducers were immersed in a water bath and positioned so that the ultrasonicenergy was focused through the water bath and bearing shell onto the lubricant layerTable 2 details the bandwidth geometry and focusing properties of the transducersused

The pulse reregected from the lubricant layer was amplishyed and stored on a dig-ital oscilloscope The stored reregected signals were passed to a PC for processingFigure 4 shows a schematic of the apparatus and data signals Software (written inthe LabView environment) was written to control the UPR receive reregection signalsfrom the oscilloscope perform the required signal processing and display the requiredresults

Proc R Soc Lond A (2003)

964 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

ball bearing

raceway

focusedultrasonictransducer

lubricant film

controlsignal

digital scope

downloadwaveform to PC

UPR

PC

Figure 4 Schematic of ultrasonic pulsing and receiving system

transducer

water tank

shim

glasssheets

positioning scale

Figure 5 Schematic of the apparatus used for generatingthin liquid macrlms between two degat surfaces

5 Measurement of a stationary liquid layer

Initial experiments were performed on thin liquid layers between stationary solidsurfaces Two conshygurations were chosen a water wedge between optical glass regatsand an oil shylm between two eccentric cylinders The former apparatus was used toproduce a wide range of measurable liquid-layer thickness The latter was designed toinvestigate the enotects of the curvature of the solid surfaces and the use of a mineraloil as the liquid medium

(a) Liquid-wedge apparatus

Shims of various thickness were used to separate sheets of regoat glass which werethen immersed in a water tank as shown in shygure 5 The ultrasonic transducerswere also immersed in the water tank and mounted above the liquid wedge on acomputer-controlled xy positioning frame The ultrasonic pulsing and receiving wascontrolled by the apparatus as shown in shygure 4

The shyrst step in the procedure was to determine the frequency characteristics of theincident ultrasonic pulse The bottom glass plate was removed and the pulse reregected

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 965

6 7 8 9 10 11

10

09

08

07

06

05

04

03

02

refl

ect

ion c

oef

fici

ent

18 mm

53 mm

89 mm

124 mm

159 mm

195 mm

(a)

10

08

06

04

02

0

refl

ect

ion c

oeff

icie

nt

15 17 19 21 23 25 27 29 31 33

f (MHz)

125 mm 375 mm 50 mm 625 mm 75 mm(b)

Figure 6 Measured redegection-coeplusmncient spectra for a range of deguid macrlm thicknesses using(a) a 10 MHz and (b) a 25 MHz centre-frequency transducer

from the glasswater interface recorded This time-domain signal was converted tothe frequency domain via a fast Fourier transform and stored as a reference Aref Inthis way

Aref(f) = I(f)Rgw (51)

where I(f ) is the frequency-response characteristic of the incident pulse and Rgw

is the glasswater reregection coemacrcient given by (21) The bottom plate was thenrepositioned and measurements of the pulse reregected from the reguid shylm were recordedat various locations along the reguid wedge This measurement signal Am eas can bewritten as

Am eas (f) = I(f)Rl(f) (52)

Proc R Soc Lond A (2003)

966 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

25

20

15

10

5

0

film

thic

knes

s (m

m)

60 65 70 75 80 85 90 95 100 105 110

f (MHz)

Figure 7 Film-thickness results determined by the application ofthe spring model to the redegection spectra of macrgure 6a

where Rl(f) is the reregection-coemacrcient spectrum of the lubricant layer which canthen be obtained by combining (51) and (52)

Rl(f) =Am eas (f)

Aref(f)Rgw (53)

Figure 6 shows two sets of reregection-coemacrcient spectra of liquid layers in a liquid-wedge experiment recorded using two dinoterent wide-band transducers for a rangeof shylm thickness The thickness of the liquid layer at any measuring location wasestimated from the geometry of the reguid wedge formed by the shim

From shygure 6b it can be seen that at higher shylm thicknesses resonant frequencies(observed as minima in the reregection-coemacrcient spectra) are visible When these res-onances occur the layer thickness can be readily determined from (23) For thinnerliquid layers andor when using lower-frequency transducers the resonance is notobserved as it occurs beyond the frequency range of the transducer However theshape of the reregection-coemacrcient spectrum below resonance can be used to predictthe thickness of the liquid layer though the application of the spring model (equa-tion (27))

The stinotness of the layer can be measured over a range of frequencies with onetransducer As the stinotness at a single frequency is sumacrcient to enable prediction ofthe reguid-layer thickness there is some redundancy in the data that can be used as amethod of checking the accuracy of the spring model Figure 7 shows the data given inshygure 6a converted to shylm thickness via (27) over the bandwidth of the transducerFrom shygure 7 it can be seen that for the lower shylm-thickness values the curvesare horizontal This indicates a good measurement as the shylm thickness cannot bea function of the frequency with which it is measured However for the top curvethe model does not correctly convert the reregection coemacrcient to a constant layerthickness This is because as the reregection coemacrcient tends to unity so the springmodel (equation (27)) becomes prone to numerical error For the next curve down

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 967

0

10

20

30

40

50

70

mea

sure

d f

ilm

thic

kness

(m

m)

60

predicted film thickness (mm)

10 20 30 40 50 60 70

Figure 8 Film-thickness values measured by ultrasonic redegection compared withpredictions of the thickness determined from the geometry of the deguid wedge

at the higher frequencies the same happens This represents a limit of the spring-model approach and to measure these thicker shylms either lower frequencies shouldbe used so R is lower or higher frequencies used and the location of resonancesdetermined

Figure 8 shows ultrasonic measurements of the thickness of the liquid shylm com-pared with the geometrical prediction of the layer thickness The data below 25 mmcorrespond to measurements performed using the spring model while the data above25 mm have been determined from the measurement of shylm resonances Agreementis good (and a straight line is observed) but in practice the measured liquid-layerthickness tends to be slightly larger than that of the shim This is likely to becaused by either some thin residual of water between the shim of the glass plateor by deformation of the shim where it has been cut Each of these enotects wouldtend to make the liquid layer thicker and hence explain the dinoterence seen in shyg-ure 8

(b) Annular oil-macrlm apparatus

Figure 9 shows the apparatus to create an oil wedge between a ring and a shaft Thering and shaft were made from aluminium The ringshaft interface had a nominaldiameter of 70 mm and a diametral clearance of 100 mm The shaft was spring loadedagainst the ring By changing the position of the loading point the gap thicknessin the region above the transducer could be varied The gap was shylled with mineraloil (Shell Turbo T68) through a small shyller hole A 25 MHz focused transducer waslocated in a water bath beneath the assembly The transducer was positioned so thatthe wave was focused on the reguid layer

Figure 10 shows a plot of the shylm thickness determined from the reregection mea-surements for various angular positions of the loading point relative to the ultra-sonic measurement position In this case all the shylms were measured using theshylm-resonance method The theoretical width of annular gap h between eccentriccylinders is obtained from geometry

h = R1

middot

1 iexcl

micro

R1 iexcl R2

R1

para2

sin2 iquest

cedil1=2

iexcl R2 + (R1 iexcl R2) cos iquest (54)

Proc R Soc Lond A (2003)

968 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

transducer

water tank

measurement zone

oil-filled annulus

tension spring

aluminium cylinders

Figure 9 Apparatus used to create an annular oil macrlm for ultrasonic-redegection experiments

film

thic

knes

s (m

m)

100

90

80

70

60

50

40

30

20

10

0

angular position (deg)

-180 -135 -90 -45 0 45 90 135 180

ultrasonic measurements

mathematical solution

Figure 10 Film-thickness values measured by ultrasonic redegection for an annular macrlm betweentwo eccentric cylinders Experimental results are compared with the geometrical solution

where R1 and R2 are the radii of the bush and shaft respectively and rsquo is theangle measured from the point of contact Equation (54) is included in shygure 10 forcomparison and a good correlation was observed

To reduce the enotects of the curvature of the lubricated interface the transducersused in this experiment focus the wave onto the oil layer The spot size of the focusedwave varies with frequency according to the relationship (Silk 1984)

df(iexcl6 d B) =1028F c

fD (55)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 969

steel disc water bath

oil meniscus

rotating steel ball

transducer

hydraulic load

motor drive

Figure 11 Schematic of the experimental apparatus used to generatean EHD macrlm for a ball sliding on a degat

where df is the diameter of the spot size (where the signal has reduced to iexcl6 dBof its peak value) F is the transducer focusing length f is the wave frequencyc is the speed of sound in water and D is the diameter of the piezoelectric elementFor a 25 MHz frequency wave this corresponds to a spot size in water of 522 mmThis is small compared with the radius of the shaftbush apparatus So essentiallythe transducer is receiving signals back from a regat region of constant shylm thick-ness and the curvature has little enotect The good agreement between experimen-tal and theoretical liquid-layer thickness shown in shygure 10 further validates thishypothesis

6 Measurement of dynamic lubricating macrlms

An EHD lubricant shylm forms between rolling or sliding non-conformal contactsTypically the thickness of the oil layer is in the region of 011 mm This is withinthe range of the possible measurement by ultrasonic means and within the spring-model regime of ultrasonic response In this work EHD shylms have been measuredin a model rig containing a single stationary lubricated contact and in a rolling-element bearing where the lubricant shylm is transient (with respect to the trans-ducer)

(a) Ball on disc EHD lubrication apparatus

Figure 11 shows the apparatus used to generate a single EHD lubricated contactA steel ball is supported on rollers and hydraulically loaded onto the underside ofa steel disc The ball is rotated at constant speed by an electric motor througha gear box and quill shaft The steel disc is held stationary such that the ball iscompletely sliding against the underside of the disc This apparatus is a modishyed`optical elastohydrodynamicrsquo apparatus (originally developed by Cameron amp Gohar(1966)) where the semi-reregective rotating glass disc has been replaced by a station-

Proc R Soc Lond A (2003)

970 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

005

010

015

020

025

030

035

040

0 02 04 06 08 10 12 14

lubri

can

t fi

lm thic

kness

(m

m)

entrainment speed (m s-1)

theoretical solution a = 015 mmmeasurements a = 015 mmtheoretical solution a = 01 mmmeasurements a = 01 mm

Figure 12 EHD lubricant-macrlm-thickness variation with ball-sliding speed for two loadsUltrasonic-redegection measurements are compared with a theoretical solution

ary steel disc and the microscope replaced by an ultrasonic transducer The balldisc contact was regooded with a mineral oil (Shell Turbo T68) which is entrainedinto the contact to form an EHD shylm A 50 MHz focused transducer was mountedabove the contact in a water bath The transducer was positioned directly abovethe contact region and at a distance such that the wave is focused on the balldiscinterface

Reregected pulses were recorded from the discball interface as the ball rotationalspeed and load were varied A reference spectrum was obtained by recording the pulsereregected when the ball was out of contact with the disc but the disc was still regoodedwith oil As in the wedge experiment the reference and lubricant-layer measurementswere used in (32) to obtain the reregection-coemacrcient spectrum of the lubricant layerA series of reregection coemacrcient spectra were then recorded from the discball contactas the sliding speed was increased The spring model (equation (27)) was used todetermine the shylm thickness from these spectra An automated LabView interfacewas written to record the spectra divide by a reference and convert the data intoshylm thickness (as shown in shygure 6) As discussed in x 3 above the density and speedof sound of the oil used in (27) are those at contact pressure (in this case 08 GPa)and not those in the bulk

Figure 12 shows the measured variation in shylm thickness determined from thereregection coemacrcient spectra as the speed is increased for two load cases (giving con-tact radii a of 01 and 015 mm) For this lubrication case a theoretical predictionof the oil-shylm thickness can be obtained from the regression equations of Dowson ampHigginson (1966) The central shylm thickness hc is expressed as a regression equationconsisting of shyve non-dimensional parameters

Hc = 269U 067G053W iexcl0067(1 iexcl 061eiexcl073k) (61)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 971

test rolling bearing

measurement zone

hydraulic loading

focusing transducer

water bath

belt and pulley drive

Figure 13 Schematic of apparatus used for ultrasonic measurementsof macrlm thickness in rolling-element bearings

where

Hc =hc

Rx

W =P

2EcurrenR2x

U =sup20u

2EcurrenRx

k = 103

micro

Ry

Rx

para064

G = 2notEcurren

where Ecurren is the reduced modulus Rx and Ry are the reduced radii in the paralleland transverse directions u is the mean surface speed P is the applied contact loadsup20 is the viscosity of oil in the inlet and not is its pressure-viscosity coemacrcient

The predictions of (61) for the two load cases are plotted in shygure 12 The agree-ment between the theoretical solution and the experimental data is good Typicallythe measured data are repeatable to within sect20 The oil shylm generated by theapparatus is not completely stable To directly observe the lubricant shylm the steeldisc was replaced by the glass disc and the shylm monitored visually A certain amountof shylm reguctuation was observed during normal running (caused by a slight processingof the ball on its supporting rollers) Notwithstanding the results are encouragingbecause this indicates that both the integrity of the ultrasonic method and alsothat the speed of sound of the lubricating oil compares well with predictions fromhigh-pressure measurements

(b) Rolling bearing lubricant-macrlm measurement

The duration of the ultrasonic pulses used in this work was short Spatially thepulse width was typically three wavelengths in length A 25 MHz wave travelling insteel results in a pulse duration of 01 ms Therefore it is feasible to record the shylmthickness in a rolling element moving past the focal point of an ultrasonic transducer

The approach has been used to measure shylm thickness in a 6410 deep-grooveball bearing Figure 13 shows a schematic of the bearing and the positioning of thetransducer The 25 MHz transducer (see table 2 for details) was located in a small

Proc R Soc Lond A (2003)

972 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

0

01

02

03

04

05

07

01 02 03 04 05 06 07

theo

reti

cal

film

thic

knes

s pre

dic

tion (

mm

)

45 kN 112 RPM 60 kN 72 RPM

60 kN 103 RPM 60 kN 128 RPM

60 kN 135 RPM 60 kN 137 RPM

60 kN 178 RPM 60 kN 195 RPM

60 kN 297 RPM 60 kN 375 RPM

75 kN 48 RPM 75 kN 124 RPM

06

measured film thickness (mm)

Figure 14 Comparison of rolling-element-bearing macrlm thickness measured byan ultrasonic means with EHD theoretical solution

water bath machined out of the bearing bush The transducer was spherically focusedand positioned in the water bath so that the wave was focused on the contact betweena ball and the raceway The bearing was loaded hydraulically and rotated by anelectric motor The bearing cavity was regooded with a mineral oil (Shell Turbo T68) Athermocouple was positioned on the outer raceway near the ultrasonic measurementpoint The bearing was loaded to give a contact eclipse between the ball and theouter raceway of semi-major and semi-minor axes 115 and 08 mm respectivelyThe bearing was then rotated and the transducer set to continuously pulse at arepetition rate of 10 kHz

The focal spot size of the transducer was ca 500 mm The maximum rotationalspeed of the bearing in these tests was 375 rpm At this rotational speed theregion of focused ultrasound would remain completely within the lubricated con-tact for ca 05 ms This allowed approximately shyve discrete pulses of ultrasound tobe reregected from the lubricant shylm as each ball passed through the measurementzone Initially a reference reregected pulse was recorded when the bearing was station-ary and there was no ball located over the measurement zone (although the cavitywas still shylled with oil) If a pulse is incident on an EHD shylm its amplitude is reducedbecause part of the wave has been transmitted through the oil shylm into the ball Bycontinuously monitoring the signals reregected from the raceway measurements of theball-raceway contacts were made Of the shyve pulses reregected from the ball-racewaycontact the lowest amplitude pulse was selected for analysis This pulse correspondsto the thinnest measured shylm thickness It should be noted that the resolution of thefocused transducer and the measurement interval are such that it was not possibleto record the horseshoe-shaped minimum shylm-thickness constriction at the contactexit The selected pulse was analysed shyrstly using (53) to calculate the reregection

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 973

film

thic

knes

s (m

m)

1000

100

10

1

01

001

00010 10 20 30 40 50 60

f (MHz)

time of flight limit

resonance method limit

spring model upper limit (R = 09)

spring model lower limit (R = 01)

Figure 15 Limits of operation for macrlm-thickness measurement by ultrasonic means

coemacrcient and then using the spring model to predict the shylm thickness The speedof sound in the oil in the contact is set to c = 4400 m siexcl1 (determined using themethod described in x 3)

Figure 14 shows the measured shylm thickness plotted against a prediction of theshylm thickness from the solution for an elliptical contact of Dowson amp Higginson(1966) (equation (61)) The bearing and lubricant heats up during operation Thetemperature of the entrained oil was monitored and used to determine an appropriateviscosity with which to calculate the shylm thickness in (61) This was why the resultswere not plotted as shylm thickness against speed (as in shygure 11) because viscositywas varying throughout the test

The results in shygure 14 show good agreement between measured lubricant-shylmthickness and that predicted by the EHD regression equations The spread along thex-axis shows the variation in shylm for nominally the same bearing operating conditions(load speed and oil temperature) At this stage it is not clear whether this scatteris a result of the measurement process or whether this is the actual shylm thicknessin the bearing It is worth noting that this measurement process could be improvedif the exact position of the ball could be related to the ultrasonic measurement soallowing a more precise measurement of the minimum shylm thickness

7 Discussion limits of operation

It is instructive to consider the limits of shylm-thickness measurement for a given ultra-sonic frequency The simplest method for determining the thickness of a lubricantlayer providing it is sumacrciently thick is by measuring the ToF through the layerA reregection occurs at the layer front face and another at the back face The thick-ness is readily obtained from the time between the arrival of these pulses multipliedby the acoustic velocity For the method to work the two reregected pulses must besumacrciently discrete and so the propagation distance must be greater than the pulse

Proc R Soc Lond A (2003)

974 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

width and so the minimum shylm thickness detectable by this method is given by

h gtnc

2f (71)

where n is the number of wavelengths in the ultrasonic pulse typically around threeThis measurement limit is plotted in shygure 15 as the minimum frequency requiredto measure a given shylm thickness Conventional ultrasonic non-destructive testingis generally restricted by losses in the propagating media (steel in this case) tofrequencies below 4060 MHz From (71) this means that the ToF method is onlypractically useful for layers of thickness greater than 40 mm This is thicker than thatfound on most commercial bearing systems

A lubricant layer resonates at a frequency given by (23) This equation also givesthe low thickness limit for this technique as the upper frequency output by a giventransducer determined the lowest measurable layer thickness This limit is also shownin shygure 15 for the shyrst through-thickness mode (ie m = 1) So using the highestpractical frequencies shylms greater than 10 mm are measurable by the shylm-resonancemethod

The upper limit of shylm thickness measurable using the spring-model approach isreached as R tends to unity in (27) Experience shows that measurements of R lessthan 09 yield satisfactory results The lowest shylm thickness measurable will dependon the smallest possible value of R This in turn will depend on the signal-to-noiseratio A signal-to-noise ratio of 60 dB is typical for conventional ultrasonic non-destructive testing systems The noise amplitude is thus 1

1000of the pulse amplitude

In the case of a measurement on a real bearing the achievable signal-to-noise ratiowill be reduced by the transducer-bearing reregection coemacrcient and by the attenuationin the bearing shell This means that the pulse incident in the reguid shylm will bereduced from that output by the transducer by a factor of shyve (as a conservativeestimate) Further it is assumed that for reliable measurements a pulse reregectedfrom the oil layer should have an amplitude approximately 20 times that of the noiselevel This results in a minimum measurable reregection coemacrcient of R = 01 Therelationships between the shylm thickness and the transducer frequency for the upperlimit when R = 09 and the lower where R = 01 are shown in shygure 15

This indicates that for a measuring frequency of 60 MHz a lubricant shylm of 2 nmis measurable This opens up the possibility of measuring boundary-type lubricantshylms between machine elements However the models presented here are designedfor a parallel-sided oil layer completely separating the smooth bearing surface If atthese low shylm thickness metal-to-metal contact occurs then transmission will occurat this location In this case some alternative method for interpreting reregectioncoemacrcients will be needed

8 Conclusions

Ultrasound is reregected from the lubricant shylm between bearing surfaces It is possibleto deduce the thickness of the lubricant shylm by comparing the frequency spectrumof the reregected pulse with that of the incident pulse The response of the lubricantlayer to an ultrasonic pulse has been modelled using both a spring-model methodand a continuum method The spring model is suitable for thin lubricant shylms inwhich the wavelength of the ultrasound is much larger than the layer thickness The

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 975

continuum model is valid for all layer thicknesses and allows the prediction of thethrough-thickness resonant frequencies of the lubricant layers Measurement of thesethrough-thickness resonances also provides a means of measuring the layer thickness

Experiments on reguid layers between regat plates and eccentric rings have demon-strated that ultrasound can suitably measure a wide range of liquid layer thicknessThe EHD lubricant shylm that forms between a ball sliding on a regat surface hasalso been measured ultrasonically The measured results agree well with theoreti-cal predictions taking into account the greatly increased speed of sound throughthe lubricant when it is under high pressure Films in the range 50500 nm wererecorded

The approach can also be used to measure shylm thickness in a rolling-elementbearing An ultrasonic transducer was mounted on the bearing raceway and thepulse reregected from the lubricant layer generated as the ball passes was recordedAgain measured results agreed well with theoretical predictions

The lower limit of measurement by this method depends on the signal-to-noiseratio A continuum model showed that using frequencies up to 60 MHz permits themeasurement of 2 nm thick shylms There is no upper limit to shylm-thickness measure-ment Thick shylms (greater than 40 mm) can be measured by a time-of-regight methodFilms of intermediate thickness can be determined by measuring the frequency atwhich the shylm resonates

This work was funded by a grant from the UK Engineering and Physical Sciences ResearchCouncil under the ROPA programme The authors acknowledge the help of Phil Harper of theUniversity of Sheplusmneld for his assistance with some of the measurements

References

Astridge D G amp Longmacreld M D 1967 Capacitance measurement and oil macrlm thickness in alarge radius disc and ring machine Proc Inst Mech Engrs 182 8996

Cameron A amp Gohar R 1966 Theoretical and experimental studies of the oil macrlm in lubricatedpoint contact Proc R Soc Lond A 291 520536

Dowson D amp Higginson G R 1966 Elastohydrodynamic lubrication|the fundamentals of roller

and gear lubrication Oxford Pergamon

Drinkwater B W Dwyer-Joyce R S amp Cawley P 1996 A study of the interaction betweenultrasound and a partially contacting solidsolid interface Proc R Soc Lond A 452 26132628

El-Sisi S I amp Shawki G S A 1960 Measurement of oil-macrlm thickness between disks by electricalconductivity Trans ASME J Basic Engng 82 12

Hamilton G M amp Moore S L 1967 A modimacred gauge for investigating an elastohydrodynamiccontact Proc Inst Mech Engrs 182 251

Hamrock B J 1994 Fundamentals of deguid macrlm lubrication McGraw-Hill

Hosten B 1991 Bulk heterogeneous plane-wave propagation through viscoelastic plates andstratimacred media with large values of frequency-domain Ultrasonics 29 445450

Jacobson B O amp Vinet P 1987 A model for the indeguence of pressure on the bulk modulusand the indeguence of temperature on the solidimacrcation pressure for liquid lubricants Trans

ASME J Tribology 109 709

Johnston G J Wayte R amp Spikes H A 1991 The measurement and study of very thinlubricant macrlms in concentrated contacts Tribol Trans 34 187194

Kinra V K Jaminet P T Zhu C amp Iyer V R 1994 Simultaneous measurement of theacoustical properties of a thin-layered medium the inverse problem J Acoust Soc Am 9530593074

Proc R Soc Lond A (2003)

958 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

gears operate in the elastohydrodynamic (EHD) regime with shylms less than 1 mmthick The lubricant shylm should be thick enough to ensure separation of the surfacesbut not so thick that excessive pumping losses are incurred

There are many methods available for predicting the thickness of reguid shylms formedbetween surfaces based on Reynoldsrsquos equation (Hamrock 1994) These are now rou-tinely used in the design of bearing components However the measurement of lubri-cant shylms and certainly the online monitoring of shylm thickness in a component hasproved more dimacrcult

Existing techniques for lubricant-shylm measurement fall into two categories electri-cal methods and optical methods Early work (El-Sisi amp Shawki 1960) concentratedon the determination of the shylm thickness by measurement of its electrical resis-tance In later studies measurements of the shylm capacitance (Astridge amp Longshyeld1967) proved more enotective and the use of micro-transducers gave enhanced reso-lution (Hamilton amp Moore 1967) These methods require electrical isolation of thecontact elements and either give a composite shylm-thickness value over the wholebearing surface or require the positioning and alignment of small surface-mountedsensors The application of optical methods requires either that one of the contactelements is transparent or that it contains a transparent window Optical interfer-ometry (Cameron amp Gohar 1966) has proved successful in the measurement of EHDshylms and more recently boundary shylms (Johnston et al 1991) The use of lasers toreguoresce a lubricant shylm has also been used to determine shylm thickness (Richardsonamp Borman 1991) However the requirement for transparency has meant that thesemethods are rarely used outside the laboratory

In this paper a novel approach has been investigated in which the response ofa lubricant shylm to an ultrasonic pulse is used to determine the shylm thickness Themethod is such that it can be used with appropriate signal processing over a widerange of lubricant-shylm thickness Also because it is essentially non-invasive it canbe used to give online shylm measurement in real bearing components

2 Ultrasonic redegection from a layer

When ultrasound is incident on a boundary between two dinoterent media some of theenergy is reregected and some transmitted The reregection and transmission behaviourof displacement waves at the boundary is dependent on the acoustic properties ofthe two media The proportion of any incident signal reregected (or the reregectioncoemacrcient R) is given by the well-known equation

R =z1 iexcl z2

z1 + z2 (21)

where z is the acoustic impedance of the media (given by the product of density andspeed of sound) and the subscripts refer to the two media The proportion of theincident signal transmitted (or transmission coemacrcient T ) can then be calculated as

T = 1 iexcl R (22)

If ultrasound is incident on a multi-layered system then the signal transmittedor reregected is the superposition of the result of the application of (21) and (22) ateach boundary Figure 1 shows an ultrasonic beam incident on a typical lubricatedcontact which is a three-layered system consisting of steellubricantsteel The steel

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 959

ball bearing

raceway

focusedultrasonictransducer

lubricant film

I F B1 B2

Figure 1 Schematic of an ultrasonic beam incident on a lubricated contact

either side of the lubricant represents the bearing elements such as the bush andshaft in a journal bearing or the ball and raceway in a rolling-element bearing Asthe steel sections are large when compared to the wavelength of the ultrasound theycan be modelled as semi-inshynite If the lubricant layer is sumacrciently thick or theultrasonic wave packet small enough then the reregections from the top and bottombearing surfaces are discrete in time This means that if the speed of sound in thelubricant is known then the thickness of the lubricant shylm can be determined bymeasuring the time-of-regight (ToF) between the two reregections The amplitude ofthese reregected pulses can also be calculated from (21) and (22) assuming that thelosses in the lubricant are small This ToF approach is commonly used for thicknessgauging of metallic components and for corrosion monitoring As the lubricant shylmbecomes thinner the ToF approach becomes less accurate until for very thin layersthe reregected pulses overlap and it becomes impossible to distinguish the discretereregections Typically even the thickest lubricant shylms are less than 50 mm thick andso the ToF approach is rarely applicable

For a practical lubricant shylm the challenge is to extract the thickness informationfrom the reregections that are overlapping in the time domain There are a numberof approaches that can be adopted For example Tsukahara et al (1989) used thesurface waves generated by an acoustic microscope to characterize thin layers Inthis paper two alternative approaches are used Firstly the through-thickness reso-nances of the lubricant layer are measured and interpreted via a continuum modelSecondly if the lubricant-shylm thickness is so small that the frequency of the shyrstthrough-thickness resonance is above the measurable range the amplitude of thereregected signal can be measured and interpreted using a spring interface modelThese approaches are now discussed in detail

Many authors (Hosten 1991 Kinra et al 1994 Pialucha amp Cawley 1994) havedescribed continuum models of the multi-layered system response to ultrasonic wavesBased on continuity of stress and strain at each boundary in the multi-layered sys-

Proc R Soc Lond A (2003)

960 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

20 mm 15 mm

1 mm

01 mm

12

10

08

06

04

02

0 20 30 40 50 6010

f (MHz)

refl

ect

ion c

oeff

icie

nt

Figure 2 Continuum-model predictions of the redegection-coeplusmncient spectrumfrom a layer of mineral oil between two steel elements

Table 1 Acoustic properties of lubricating oil (Shell Turbo T68) at room temperature and

ambient and EHD pressures (estimated using the method of Jacobson amp Vinet (1987 ))

(Also included for comparison water and steel properties)

density bulk modulus wave velocityraquo (kg m iexcl 3) B (GPa) c (m s iexcl 1 )

oil at atmospheric pressure 876 184 1450

oil at 08 GPa 1002 126 3550

oil at 15 GPa 1044 212 4500

water at atmospheric pressure 1000 206 1483

steel 7923 172 5840

tem these models can be used to predict the reregection and transmission of planewaves through a given system Figure 2 shows a continuum-model prediction of thereregection coemacrcient spectrum for 01 10 15 and 20 mm thickness mineral oil layersbetween two steel half-spaces The material properties used in this calculation areshown in table 1 This is essentially the impulse response function of the systemie it gives the response of the system for an incident wave of unit amplitude In shyg-ure 2 the resonant frequencies are seen as sharp minima in the reregection-coemacrcientspectrum The minima seen at 363 MHz corresponds to a lubricant-shylm thicknessof 20 mm

Pialucha et al (1989) used a continuum-model approach to show that the reso-nant frequencies of an embedded layer are related to its thickness h and acousticproperties by

h =cm

2fm (23)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 961

where c is the speed of sound in the lubricant layer m is the mode number of theresonant frequency and fm is the resonant frequency (in Hz) of the mth mode It canbe seen from consideration of (23) that higher resonant frequencies correspond tothinner lubricant shylms The thinnest shylm measurable by this approach is then limitedby the upper operating frequency In practice the frequency is limited to below 4060 MHz by the attenuation of the ultrasonic pulse in the bearing materials Thismeans that if the lubricant layer is below 10 mm the resonant frequency will beabove the measurable range

The region below the shyrst resonance of a simple mass-spring system is known asthe stinotness-controlled region because the deregection of the mass is dependent purelyon the applied load and the spring stinotness In the same way it can be shown (Hosten1991) that the interaction of ultrasound with a very thin layer (which would havea very high shyrst resonant frequency) is governed by the stinotness of that layer Thestinotness per unit area K of a thin layer is given by

K =raquoc2

h (24)

where raquo is the density of the layer and c the speed of sound in the layer This springstinotness can then be used in a quasi-static model of the interaction of ultrasound withthe lubricant layer In this way Tattersall (1973) demonstrated that the reregectioncoemacrcient of the layer was given by the expression

R =z1 iexcl z2 + i(z1z2=K)

z1 + z2 + i(z1z2=K) (25)

where z1 and z2 refer to the acoustic impedance of the materials either side of thelubricant layer For identical materials either side of the lubricant shylm (z1 = z2 = z 0)this reduces to

R =1

p

1 + (K=ordmfz0) (26)

Drinkwater et al (1996) used the above analysis to determine the stinotness of drycontacts in which the interface between two rough surfaces composed of air gapsand regions of asperity contact acts like a layer of reduced stinotness Measurementof the reregection coemacrcient and hence interface stinotness can give information aboutthe degree of conformity of the contacting surfaces

Figure 3 shows a comparison between the spring-model prediction and thecontinuum-model prediction for the reregection-coemacrcient spectra from a mineral oillayer surrounded by steel It can be seen that the agreement between the two modelsat frequencies below resonance is excellent In fact within the accuracy of the com-puter the predictions are identical if f lt 1

2f1 Combining equations (24) and (26)

the thickness of the layer is related to the reregection coemacrcient by

h =raquoc2

ordmfz 0

micro

R2

1 iexcl R2

para

(27)

From (27) it can be seen that as R approaches unity so the calculated thicknessapproaches inshynity In practical measurement this means that the spring approachloses accuracy as the reregection coemacrcient approaches unity The authors have foundthat for practical purposes R lt 09 gives satisfactory results

Proc R Soc Lond A (2003)

962 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

12

10

08

06

04

02

0 10 20 30 40 50

f (MHz)

refl

ecti

on c

oeff

icie

nt

spring model

continuum model

Figure 3 Comparison between spring-model and continuum-model predictions for theredegection-coeplusmncient spectra from a mineral oil macrlm between two steel elements

3 Acoustic properties of a lubricant macrlm

To determine the thickness of a lubricant shylm using (27) it is necessary to knowboth the density of and the speed of sound through the lubricant The speed ofsound can readily be determined for oil in the bulk from a simple ToF measurementbetween a transducer and a regat reregector For the oil used in these experiments (ShellTurbo T68) the acoustic properties at 20 macrC are shown in table 1

This value is suitable for the analysis of ambient reguid wedges or low-pressurehydrodynamic lubricant shylms However in EHD shylms the lubricant is subjectedto pressures high enough to cause solidishycation and a signishycant change in physi-cal properties The speed of sound through oil under EHD conditions is thereforevery dinoterent to those in the bulk The speed of propagation of a longitudinal wavethrough a medium depends on the density raquo and the bulk modulus B accordingto (see for example Povey 1997)

c =

s

B

raquo (31)

Jacobson amp Vinet (1987) provide a model to determine the inreguence of pressureon the compression and bulk modulus of liquid lubricants They give an equation ofstate to describe the behaviour of the lubricant under pressure p

p =3B0

x2(1 iexcl x)esup2(1iexclx) (32)

and the bulk modulus under pressure is given by

B =B0

x2[2 + (sup2 iexcl 1)x iexcl sup2x2]esup2(1iexclx) (33)

where B0 is the bulk modulus at zero pressure sup2 is a lubricant-specishyc parameterand x is a function of the relative compression

x = 3

r

raquo0

raquop (34)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 963

Table 2 Details of the transducers used in this work

(The focal length and spot size (equation (55)) are determined for a centre-frequency wave inwater)

bandwidth focal length spot sizecentre frequency (iexcl6 dB points) element diameter (in water) (in water)

f (MHz) (MHz) D (mm) F (mm) df (mm)

10 417 127 76 921

25 1732 635 54 522

50 4075 635 25 121

where raquo0 is the density at zero pressure and raquop the density at pressure p These equa-tions are used for the oil both in its liquid state and after it undergoes solidishycationbut employing dinoterent values of sup2 and B0

Jacobson amp Vinet used a high-pressure chamber to measure the compression ofseveral liquid lubricants up to pressures of 22 GPa and determined the parametersfor (32) and (33) For mineral oils the bulk modulus increased from 1517 GPaat atmospheric pressure to 2030 GPa at EHD pressures while the density increasedby 2030 Therefore from (31) the speed of sound within an EHD contact is likelyto be some two to four times greater than that under ambient conditions

Unfortunately there are no test data available specishycally for the lubricant usedin these studies (Shell Turbo T68) However parameters from a similar base oil(extracted from Jacobson amp Vinet (1987)) have been used to determine the relation-ship between bulk modulus density change and pressure Table 1 shows the resultsof this analysis for two oil pressures the lower corresponding to that experienced inthe ball on regat apparatus and the higher to that in ball-bearing contact

4 Ultrasonic redegection measurement apparatus

An ultrasonic pulser-receiver (UPR) generates a high-voltage pulse that causes apiezoelectric transducer to be excited in mechanical resonance The transducer thenemits a broadband pulse of ultrasonic energy As can be seen in shygure 1 this ultra-sonic pulse propagates through the bearing shell is reregected from the lubricant layerand is received by the same transducer Measurements were made using focused ultra-sonic transducers with a range of dinoterent centre frequencies (10 25 and 50 MHz)The transducers were immersed in a water bath and positioned so that the ultrasonicenergy was focused through the water bath and bearing shell onto the lubricant layerTable 2 details the bandwidth geometry and focusing properties of the transducersused

The pulse reregected from the lubricant layer was amplishyed and stored on a dig-ital oscilloscope The stored reregected signals were passed to a PC for processingFigure 4 shows a schematic of the apparatus and data signals Software (written inthe LabView environment) was written to control the UPR receive reregection signalsfrom the oscilloscope perform the required signal processing and display the requiredresults

Proc R Soc Lond A (2003)

964 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

ball bearing

raceway

focusedultrasonictransducer

lubricant film

controlsignal

digital scope

downloadwaveform to PC

UPR

PC

Figure 4 Schematic of ultrasonic pulsing and receiving system

transducer

water tank

shim

glasssheets

positioning scale

Figure 5 Schematic of the apparatus used for generatingthin liquid macrlms between two degat surfaces

5 Measurement of a stationary liquid layer

Initial experiments were performed on thin liquid layers between stationary solidsurfaces Two conshygurations were chosen a water wedge between optical glass regatsand an oil shylm between two eccentric cylinders The former apparatus was used toproduce a wide range of measurable liquid-layer thickness The latter was designed toinvestigate the enotects of the curvature of the solid surfaces and the use of a mineraloil as the liquid medium

(a) Liquid-wedge apparatus

Shims of various thickness were used to separate sheets of regoat glass which werethen immersed in a water tank as shown in shygure 5 The ultrasonic transducerswere also immersed in the water tank and mounted above the liquid wedge on acomputer-controlled xy positioning frame The ultrasonic pulsing and receiving wascontrolled by the apparatus as shown in shygure 4

The shyrst step in the procedure was to determine the frequency characteristics of theincident ultrasonic pulse The bottom glass plate was removed and the pulse reregected

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 965

6 7 8 9 10 11

10

09

08

07

06

05

04

03

02

refl

ect

ion c

oef

fici

ent

18 mm

53 mm

89 mm

124 mm

159 mm

195 mm

(a)

10

08

06

04

02

0

refl

ect

ion c

oeff

icie

nt

15 17 19 21 23 25 27 29 31 33

f (MHz)

125 mm 375 mm 50 mm 625 mm 75 mm(b)

Figure 6 Measured redegection-coeplusmncient spectra for a range of deguid macrlm thicknesses using(a) a 10 MHz and (b) a 25 MHz centre-frequency transducer

from the glasswater interface recorded This time-domain signal was converted tothe frequency domain via a fast Fourier transform and stored as a reference Aref Inthis way

Aref(f) = I(f)Rgw (51)

where I(f ) is the frequency-response characteristic of the incident pulse and Rgw

is the glasswater reregection coemacrcient given by (21) The bottom plate was thenrepositioned and measurements of the pulse reregected from the reguid shylm were recordedat various locations along the reguid wedge This measurement signal Am eas can bewritten as

Am eas (f) = I(f)Rl(f) (52)

Proc R Soc Lond A (2003)

966 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

25

20

15

10

5

0

film

thic

knes

s (m

m)

60 65 70 75 80 85 90 95 100 105 110

f (MHz)

Figure 7 Film-thickness results determined by the application ofthe spring model to the redegection spectra of macrgure 6a

where Rl(f) is the reregection-coemacrcient spectrum of the lubricant layer which canthen be obtained by combining (51) and (52)

Rl(f) =Am eas (f)

Aref(f)Rgw (53)

Figure 6 shows two sets of reregection-coemacrcient spectra of liquid layers in a liquid-wedge experiment recorded using two dinoterent wide-band transducers for a rangeof shylm thickness The thickness of the liquid layer at any measuring location wasestimated from the geometry of the reguid wedge formed by the shim

From shygure 6b it can be seen that at higher shylm thicknesses resonant frequencies(observed as minima in the reregection-coemacrcient spectra) are visible When these res-onances occur the layer thickness can be readily determined from (23) For thinnerliquid layers andor when using lower-frequency transducers the resonance is notobserved as it occurs beyond the frequency range of the transducer However theshape of the reregection-coemacrcient spectrum below resonance can be used to predictthe thickness of the liquid layer though the application of the spring model (equa-tion (27))

The stinotness of the layer can be measured over a range of frequencies with onetransducer As the stinotness at a single frequency is sumacrcient to enable prediction ofthe reguid-layer thickness there is some redundancy in the data that can be used as amethod of checking the accuracy of the spring model Figure 7 shows the data given inshygure 6a converted to shylm thickness via (27) over the bandwidth of the transducerFrom shygure 7 it can be seen that for the lower shylm-thickness values the curvesare horizontal This indicates a good measurement as the shylm thickness cannot bea function of the frequency with which it is measured However for the top curvethe model does not correctly convert the reregection coemacrcient to a constant layerthickness This is because as the reregection coemacrcient tends to unity so the springmodel (equation (27)) becomes prone to numerical error For the next curve down

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 967

0

10

20

30

40

50

70

mea

sure

d f

ilm

thic

kness

(m

m)

60

predicted film thickness (mm)

10 20 30 40 50 60 70

Figure 8 Film-thickness values measured by ultrasonic redegection compared withpredictions of the thickness determined from the geometry of the deguid wedge

at the higher frequencies the same happens This represents a limit of the spring-model approach and to measure these thicker shylms either lower frequencies shouldbe used so R is lower or higher frequencies used and the location of resonancesdetermined

Figure 8 shows ultrasonic measurements of the thickness of the liquid shylm com-pared with the geometrical prediction of the layer thickness The data below 25 mmcorrespond to measurements performed using the spring model while the data above25 mm have been determined from the measurement of shylm resonances Agreementis good (and a straight line is observed) but in practice the measured liquid-layerthickness tends to be slightly larger than that of the shim This is likely to becaused by either some thin residual of water between the shim of the glass plateor by deformation of the shim where it has been cut Each of these enotects wouldtend to make the liquid layer thicker and hence explain the dinoterence seen in shyg-ure 8

(b) Annular oil-macrlm apparatus

Figure 9 shows the apparatus to create an oil wedge between a ring and a shaft Thering and shaft were made from aluminium The ringshaft interface had a nominaldiameter of 70 mm and a diametral clearance of 100 mm The shaft was spring loadedagainst the ring By changing the position of the loading point the gap thicknessin the region above the transducer could be varied The gap was shylled with mineraloil (Shell Turbo T68) through a small shyller hole A 25 MHz focused transducer waslocated in a water bath beneath the assembly The transducer was positioned so thatthe wave was focused on the reguid layer

Figure 10 shows a plot of the shylm thickness determined from the reregection mea-surements for various angular positions of the loading point relative to the ultra-sonic measurement position In this case all the shylms were measured using theshylm-resonance method The theoretical width of annular gap h between eccentriccylinders is obtained from geometry

h = R1

middot

1 iexcl

micro

R1 iexcl R2

R1

para2

sin2 iquest

cedil1=2

iexcl R2 + (R1 iexcl R2) cos iquest (54)

Proc R Soc Lond A (2003)

968 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

transducer

water tank

measurement zone

oil-filled annulus

tension spring

aluminium cylinders

Figure 9 Apparatus used to create an annular oil macrlm for ultrasonic-redegection experiments

film

thic

knes

s (m

m)

100

90

80

70

60

50

40

30

20

10

0

angular position (deg)

-180 -135 -90 -45 0 45 90 135 180

ultrasonic measurements

mathematical solution

Figure 10 Film-thickness values measured by ultrasonic redegection for an annular macrlm betweentwo eccentric cylinders Experimental results are compared with the geometrical solution

where R1 and R2 are the radii of the bush and shaft respectively and rsquo is theangle measured from the point of contact Equation (54) is included in shygure 10 forcomparison and a good correlation was observed

To reduce the enotects of the curvature of the lubricated interface the transducersused in this experiment focus the wave onto the oil layer The spot size of the focusedwave varies with frequency according to the relationship (Silk 1984)

df(iexcl6 d B) =1028F c

fD (55)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 969

steel disc water bath

oil meniscus

rotating steel ball

transducer

hydraulic load

motor drive

Figure 11 Schematic of the experimental apparatus used to generatean EHD macrlm for a ball sliding on a degat

where df is the diameter of the spot size (where the signal has reduced to iexcl6 dBof its peak value) F is the transducer focusing length f is the wave frequencyc is the speed of sound in water and D is the diameter of the piezoelectric elementFor a 25 MHz frequency wave this corresponds to a spot size in water of 522 mmThis is small compared with the radius of the shaftbush apparatus So essentiallythe transducer is receiving signals back from a regat region of constant shylm thick-ness and the curvature has little enotect The good agreement between experimen-tal and theoretical liquid-layer thickness shown in shygure 10 further validates thishypothesis

6 Measurement of dynamic lubricating macrlms

An EHD lubricant shylm forms between rolling or sliding non-conformal contactsTypically the thickness of the oil layer is in the region of 011 mm This is withinthe range of the possible measurement by ultrasonic means and within the spring-model regime of ultrasonic response In this work EHD shylms have been measuredin a model rig containing a single stationary lubricated contact and in a rolling-element bearing where the lubricant shylm is transient (with respect to the trans-ducer)

(a) Ball on disc EHD lubrication apparatus

Figure 11 shows the apparatus used to generate a single EHD lubricated contactA steel ball is supported on rollers and hydraulically loaded onto the underside ofa steel disc The ball is rotated at constant speed by an electric motor througha gear box and quill shaft The steel disc is held stationary such that the ball iscompletely sliding against the underside of the disc This apparatus is a modishyed`optical elastohydrodynamicrsquo apparatus (originally developed by Cameron amp Gohar(1966)) where the semi-reregective rotating glass disc has been replaced by a station-

Proc R Soc Lond A (2003)

970 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

005

010

015

020

025

030

035

040

0 02 04 06 08 10 12 14

lubri

can

t fi

lm thic

kness

(m

m)

entrainment speed (m s-1)

theoretical solution a = 015 mmmeasurements a = 015 mmtheoretical solution a = 01 mmmeasurements a = 01 mm

Figure 12 EHD lubricant-macrlm-thickness variation with ball-sliding speed for two loadsUltrasonic-redegection measurements are compared with a theoretical solution

ary steel disc and the microscope replaced by an ultrasonic transducer The balldisc contact was regooded with a mineral oil (Shell Turbo T68) which is entrainedinto the contact to form an EHD shylm A 50 MHz focused transducer was mountedabove the contact in a water bath The transducer was positioned directly abovethe contact region and at a distance such that the wave is focused on the balldiscinterface

Reregected pulses were recorded from the discball interface as the ball rotationalspeed and load were varied A reference spectrum was obtained by recording the pulsereregected when the ball was out of contact with the disc but the disc was still regoodedwith oil As in the wedge experiment the reference and lubricant-layer measurementswere used in (32) to obtain the reregection-coemacrcient spectrum of the lubricant layerA series of reregection coemacrcient spectra were then recorded from the discball contactas the sliding speed was increased The spring model (equation (27)) was used todetermine the shylm thickness from these spectra An automated LabView interfacewas written to record the spectra divide by a reference and convert the data intoshylm thickness (as shown in shygure 6) As discussed in x 3 above the density and speedof sound of the oil used in (27) are those at contact pressure (in this case 08 GPa)and not those in the bulk

Figure 12 shows the measured variation in shylm thickness determined from thereregection coemacrcient spectra as the speed is increased for two load cases (giving con-tact radii a of 01 and 015 mm) For this lubrication case a theoretical predictionof the oil-shylm thickness can be obtained from the regression equations of Dowson ampHigginson (1966) The central shylm thickness hc is expressed as a regression equationconsisting of shyve non-dimensional parameters

Hc = 269U 067G053W iexcl0067(1 iexcl 061eiexcl073k) (61)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 971

test rolling bearing

measurement zone

hydraulic loading

focusing transducer

water bath

belt and pulley drive

Figure 13 Schematic of apparatus used for ultrasonic measurementsof macrlm thickness in rolling-element bearings

where

Hc =hc

Rx

W =P

2EcurrenR2x

U =sup20u

2EcurrenRx

k = 103

micro

Ry

Rx

para064

G = 2notEcurren

where Ecurren is the reduced modulus Rx and Ry are the reduced radii in the paralleland transverse directions u is the mean surface speed P is the applied contact loadsup20 is the viscosity of oil in the inlet and not is its pressure-viscosity coemacrcient

The predictions of (61) for the two load cases are plotted in shygure 12 The agree-ment between the theoretical solution and the experimental data is good Typicallythe measured data are repeatable to within sect20 The oil shylm generated by theapparatus is not completely stable To directly observe the lubricant shylm the steeldisc was replaced by the glass disc and the shylm monitored visually A certain amountof shylm reguctuation was observed during normal running (caused by a slight processingof the ball on its supporting rollers) Notwithstanding the results are encouragingbecause this indicates that both the integrity of the ultrasonic method and alsothat the speed of sound of the lubricating oil compares well with predictions fromhigh-pressure measurements

(b) Rolling bearing lubricant-macrlm measurement

The duration of the ultrasonic pulses used in this work was short Spatially thepulse width was typically three wavelengths in length A 25 MHz wave travelling insteel results in a pulse duration of 01 ms Therefore it is feasible to record the shylmthickness in a rolling element moving past the focal point of an ultrasonic transducer

The approach has been used to measure shylm thickness in a 6410 deep-grooveball bearing Figure 13 shows a schematic of the bearing and the positioning of thetransducer The 25 MHz transducer (see table 2 for details) was located in a small

Proc R Soc Lond A (2003)

972 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

0

01

02

03

04

05

07

01 02 03 04 05 06 07

theo

reti

cal

film

thic

knes

s pre

dic

tion (

mm

)

45 kN 112 RPM 60 kN 72 RPM

60 kN 103 RPM 60 kN 128 RPM

60 kN 135 RPM 60 kN 137 RPM

60 kN 178 RPM 60 kN 195 RPM

60 kN 297 RPM 60 kN 375 RPM

75 kN 48 RPM 75 kN 124 RPM

06

measured film thickness (mm)

Figure 14 Comparison of rolling-element-bearing macrlm thickness measured byan ultrasonic means with EHD theoretical solution

water bath machined out of the bearing bush The transducer was spherically focusedand positioned in the water bath so that the wave was focused on the contact betweena ball and the raceway The bearing was loaded hydraulically and rotated by anelectric motor The bearing cavity was regooded with a mineral oil (Shell Turbo T68) Athermocouple was positioned on the outer raceway near the ultrasonic measurementpoint The bearing was loaded to give a contact eclipse between the ball and theouter raceway of semi-major and semi-minor axes 115 and 08 mm respectivelyThe bearing was then rotated and the transducer set to continuously pulse at arepetition rate of 10 kHz

The focal spot size of the transducer was ca 500 mm The maximum rotationalspeed of the bearing in these tests was 375 rpm At this rotational speed theregion of focused ultrasound would remain completely within the lubricated con-tact for ca 05 ms This allowed approximately shyve discrete pulses of ultrasound tobe reregected from the lubricant shylm as each ball passed through the measurementzone Initially a reference reregected pulse was recorded when the bearing was station-ary and there was no ball located over the measurement zone (although the cavitywas still shylled with oil) If a pulse is incident on an EHD shylm its amplitude is reducedbecause part of the wave has been transmitted through the oil shylm into the ball Bycontinuously monitoring the signals reregected from the raceway measurements of theball-raceway contacts were made Of the shyve pulses reregected from the ball-racewaycontact the lowest amplitude pulse was selected for analysis This pulse correspondsto the thinnest measured shylm thickness It should be noted that the resolution of thefocused transducer and the measurement interval are such that it was not possibleto record the horseshoe-shaped minimum shylm-thickness constriction at the contactexit The selected pulse was analysed shyrstly using (53) to calculate the reregection

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 973

film

thic

knes

s (m

m)

1000

100

10

1

01

001

00010 10 20 30 40 50 60

f (MHz)

time of flight limit

resonance method limit

spring model upper limit (R = 09)

spring model lower limit (R = 01)

Figure 15 Limits of operation for macrlm-thickness measurement by ultrasonic means

coemacrcient and then using the spring model to predict the shylm thickness The speedof sound in the oil in the contact is set to c = 4400 m siexcl1 (determined using themethod described in x 3)

Figure 14 shows the measured shylm thickness plotted against a prediction of theshylm thickness from the solution for an elliptical contact of Dowson amp Higginson(1966) (equation (61)) The bearing and lubricant heats up during operation Thetemperature of the entrained oil was monitored and used to determine an appropriateviscosity with which to calculate the shylm thickness in (61) This was why the resultswere not plotted as shylm thickness against speed (as in shygure 11) because viscositywas varying throughout the test

The results in shygure 14 show good agreement between measured lubricant-shylmthickness and that predicted by the EHD regression equations The spread along thex-axis shows the variation in shylm for nominally the same bearing operating conditions(load speed and oil temperature) At this stage it is not clear whether this scatteris a result of the measurement process or whether this is the actual shylm thicknessin the bearing It is worth noting that this measurement process could be improvedif the exact position of the ball could be related to the ultrasonic measurement soallowing a more precise measurement of the minimum shylm thickness

7 Discussion limits of operation

It is instructive to consider the limits of shylm-thickness measurement for a given ultra-sonic frequency The simplest method for determining the thickness of a lubricantlayer providing it is sumacrciently thick is by measuring the ToF through the layerA reregection occurs at the layer front face and another at the back face The thick-ness is readily obtained from the time between the arrival of these pulses multipliedby the acoustic velocity For the method to work the two reregected pulses must besumacrciently discrete and so the propagation distance must be greater than the pulse

Proc R Soc Lond A (2003)

974 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

width and so the minimum shylm thickness detectable by this method is given by

h gtnc

2f (71)

where n is the number of wavelengths in the ultrasonic pulse typically around threeThis measurement limit is plotted in shygure 15 as the minimum frequency requiredto measure a given shylm thickness Conventional ultrasonic non-destructive testingis generally restricted by losses in the propagating media (steel in this case) tofrequencies below 4060 MHz From (71) this means that the ToF method is onlypractically useful for layers of thickness greater than 40 mm This is thicker than thatfound on most commercial bearing systems

A lubricant layer resonates at a frequency given by (23) This equation also givesthe low thickness limit for this technique as the upper frequency output by a giventransducer determined the lowest measurable layer thickness This limit is also shownin shygure 15 for the shyrst through-thickness mode (ie m = 1) So using the highestpractical frequencies shylms greater than 10 mm are measurable by the shylm-resonancemethod

The upper limit of shylm thickness measurable using the spring-model approach isreached as R tends to unity in (27) Experience shows that measurements of R lessthan 09 yield satisfactory results The lowest shylm thickness measurable will dependon the smallest possible value of R This in turn will depend on the signal-to-noiseratio A signal-to-noise ratio of 60 dB is typical for conventional ultrasonic non-destructive testing systems The noise amplitude is thus 1

1000of the pulse amplitude

In the case of a measurement on a real bearing the achievable signal-to-noise ratiowill be reduced by the transducer-bearing reregection coemacrcient and by the attenuationin the bearing shell This means that the pulse incident in the reguid shylm will bereduced from that output by the transducer by a factor of shyve (as a conservativeestimate) Further it is assumed that for reliable measurements a pulse reregectedfrom the oil layer should have an amplitude approximately 20 times that of the noiselevel This results in a minimum measurable reregection coemacrcient of R = 01 Therelationships between the shylm thickness and the transducer frequency for the upperlimit when R = 09 and the lower where R = 01 are shown in shygure 15

This indicates that for a measuring frequency of 60 MHz a lubricant shylm of 2 nmis measurable This opens up the possibility of measuring boundary-type lubricantshylms between machine elements However the models presented here are designedfor a parallel-sided oil layer completely separating the smooth bearing surface If atthese low shylm thickness metal-to-metal contact occurs then transmission will occurat this location In this case some alternative method for interpreting reregectioncoemacrcients will be needed

8 Conclusions

Ultrasound is reregected from the lubricant shylm between bearing surfaces It is possibleto deduce the thickness of the lubricant shylm by comparing the frequency spectrumof the reregected pulse with that of the incident pulse The response of the lubricantlayer to an ultrasonic pulse has been modelled using both a spring-model methodand a continuum method The spring model is suitable for thin lubricant shylms inwhich the wavelength of the ultrasound is much larger than the layer thickness The

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 975

continuum model is valid for all layer thicknesses and allows the prediction of thethrough-thickness resonant frequencies of the lubricant layers Measurement of thesethrough-thickness resonances also provides a means of measuring the layer thickness

Experiments on reguid layers between regat plates and eccentric rings have demon-strated that ultrasound can suitably measure a wide range of liquid layer thicknessThe EHD lubricant shylm that forms between a ball sliding on a regat surface hasalso been measured ultrasonically The measured results agree well with theoreti-cal predictions taking into account the greatly increased speed of sound throughthe lubricant when it is under high pressure Films in the range 50500 nm wererecorded

The approach can also be used to measure shylm thickness in a rolling-elementbearing An ultrasonic transducer was mounted on the bearing raceway and thepulse reregected from the lubricant layer generated as the ball passes was recordedAgain measured results agreed well with theoretical predictions

The lower limit of measurement by this method depends on the signal-to-noiseratio A continuum model showed that using frequencies up to 60 MHz permits themeasurement of 2 nm thick shylms There is no upper limit to shylm-thickness measure-ment Thick shylms (greater than 40 mm) can be measured by a time-of-regight methodFilms of intermediate thickness can be determined by measuring the frequency atwhich the shylm resonates

This work was funded by a grant from the UK Engineering and Physical Sciences ResearchCouncil under the ROPA programme The authors acknowledge the help of Phil Harper of theUniversity of Sheplusmneld for his assistance with some of the measurements

References

Astridge D G amp Longmacreld M D 1967 Capacitance measurement and oil macrlm thickness in alarge radius disc and ring machine Proc Inst Mech Engrs 182 8996

Cameron A amp Gohar R 1966 Theoretical and experimental studies of the oil macrlm in lubricatedpoint contact Proc R Soc Lond A 291 520536

Dowson D amp Higginson G R 1966 Elastohydrodynamic lubrication|the fundamentals of roller

and gear lubrication Oxford Pergamon

Drinkwater B W Dwyer-Joyce R S amp Cawley P 1996 A study of the interaction betweenultrasound and a partially contacting solidsolid interface Proc R Soc Lond A 452 26132628

El-Sisi S I amp Shawki G S A 1960 Measurement of oil-macrlm thickness between disks by electricalconductivity Trans ASME J Basic Engng 82 12

Hamilton G M amp Moore S L 1967 A modimacred gauge for investigating an elastohydrodynamiccontact Proc Inst Mech Engrs 182 251

Hamrock B J 1994 Fundamentals of deguid macrlm lubrication McGraw-Hill

Hosten B 1991 Bulk heterogeneous plane-wave propagation through viscoelastic plates andstratimacred media with large values of frequency-domain Ultrasonics 29 445450

Jacobson B O amp Vinet P 1987 A model for the indeguence of pressure on the bulk modulusand the indeguence of temperature on the solidimacrcation pressure for liquid lubricants Trans

ASME J Tribology 109 709

Johnston G J Wayte R amp Spikes H A 1991 The measurement and study of very thinlubricant macrlms in concentrated contacts Tribol Trans 34 187194

Kinra V K Jaminet P T Zhu C amp Iyer V R 1994 Simultaneous measurement of theacoustical properties of a thin-layered medium the inverse problem J Acoust Soc Am 9530593074

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 959

ball bearing

raceway

focusedultrasonictransducer

lubricant film

I F B1 B2

Figure 1 Schematic of an ultrasonic beam incident on a lubricated contact

either side of the lubricant represents the bearing elements such as the bush andshaft in a journal bearing or the ball and raceway in a rolling-element bearing Asthe steel sections are large when compared to the wavelength of the ultrasound theycan be modelled as semi-inshynite If the lubricant layer is sumacrciently thick or theultrasonic wave packet small enough then the reregections from the top and bottombearing surfaces are discrete in time This means that if the speed of sound in thelubricant is known then the thickness of the lubricant shylm can be determined bymeasuring the time-of-regight (ToF) between the two reregections The amplitude ofthese reregected pulses can also be calculated from (21) and (22) assuming that thelosses in the lubricant are small This ToF approach is commonly used for thicknessgauging of metallic components and for corrosion monitoring As the lubricant shylmbecomes thinner the ToF approach becomes less accurate until for very thin layersthe reregected pulses overlap and it becomes impossible to distinguish the discretereregections Typically even the thickest lubricant shylms are less than 50 mm thick andso the ToF approach is rarely applicable

For a practical lubricant shylm the challenge is to extract the thickness informationfrom the reregections that are overlapping in the time domain There are a numberof approaches that can be adopted For example Tsukahara et al (1989) used thesurface waves generated by an acoustic microscope to characterize thin layers Inthis paper two alternative approaches are used Firstly the through-thickness reso-nances of the lubricant layer are measured and interpreted via a continuum modelSecondly if the lubricant-shylm thickness is so small that the frequency of the shyrstthrough-thickness resonance is above the measurable range the amplitude of thereregected signal can be measured and interpreted using a spring interface modelThese approaches are now discussed in detail

Many authors (Hosten 1991 Kinra et al 1994 Pialucha amp Cawley 1994) havedescribed continuum models of the multi-layered system response to ultrasonic wavesBased on continuity of stress and strain at each boundary in the multi-layered sys-

Proc R Soc Lond A (2003)

960 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

20 mm 15 mm

1 mm

01 mm

12

10

08

06

04

02

0 20 30 40 50 6010

f (MHz)

refl

ect

ion c

oeff

icie

nt

Figure 2 Continuum-model predictions of the redegection-coeplusmncient spectrumfrom a layer of mineral oil between two steel elements

Table 1 Acoustic properties of lubricating oil (Shell Turbo T68) at room temperature and

ambient and EHD pressures (estimated using the method of Jacobson amp Vinet (1987 ))

(Also included for comparison water and steel properties)

density bulk modulus wave velocityraquo (kg m iexcl 3) B (GPa) c (m s iexcl 1 )

oil at atmospheric pressure 876 184 1450

oil at 08 GPa 1002 126 3550

oil at 15 GPa 1044 212 4500

water at atmospheric pressure 1000 206 1483

steel 7923 172 5840

tem these models can be used to predict the reregection and transmission of planewaves through a given system Figure 2 shows a continuum-model prediction of thereregection coemacrcient spectrum for 01 10 15 and 20 mm thickness mineral oil layersbetween two steel half-spaces The material properties used in this calculation areshown in table 1 This is essentially the impulse response function of the systemie it gives the response of the system for an incident wave of unit amplitude In shyg-ure 2 the resonant frequencies are seen as sharp minima in the reregection-coemacrcientspectrum The minima seen at 363 MHz corresponds to a lubricant-shylm thicknessof 20 mm

Pialucha et al (1989) used a continuum-model approach to show that the reso-nant frequencies of an embedded layer are related to its thickness h and acousticproperties by

h =cm

2fm (23)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 961

where c is the speed of sound in the lubricant layer m is the mode number of theresonant frequency and fm is the resonant frequency (in Hz) of the mth mode It canbe seen from consideration of (23) that higher resonant frequencies correspond tothinner lubricant shylms The thinnest shylm measurable by this approach is then limitedby the upper operating frequency In practice the frequency is limited to below 4060 MHz by the attenuation of the ultrasonic pulse in the bearing materials Thismeans that if the lubricant layer is below 10 mm the resonant frequency will beabove the measurable range

The region below the shyrst resonance of a simple mass-spring system is known asthe stinotness-controlled region because the deregection of the mass is dependent purelyon the applied load and the spring stinotness In the same way it can be shown (Hosten1991) that the interaction of ultrasound with a very thin layer (which would havea very high shyrst resonant frequency) is governed by the stinotness of that layer Thestinotness per unit area K of a thin layer is given by

K =raquoc2

h (24)

where raquo is the density of the layer and c the speed of sound in the layer This springstinotness can then be used in a quasi-static model of the interaction of ultrasound withthe lubricant layer In this way Tattersall (1973) demonstrated that the reregectioncoemacrcient of the layer was given by the expression

R =z1 iexcl z2 + i(z1z2=K)

z1 + z2 + i(z1z2=K) (25)

where z1 and z2 refer to the acoustic impedance of the materials either side of thelubricant layer For identical materials either side of the lubricant shylm (z1 = z2 = z 0)this reduces to

R =1

p

1 + (K=ordmfz0) (26)

Drinkwater et al (1996) used the above analysis to determine the stinotness of drycontacts in which the interface between two rough surfaces composed of air gapsand regions of asperity contact acts like a layer of reduced stinotness Measurementof the reregection coemacrcient and hence interface stinotness can give information aboutthe degree of conformity of the contacting surfaces

Figure 3 shows a comparison between the spring-model prediction and thecontinuum-model prediction for the reregection-coemacrcient spectra from a mineral oillayer surrounded by steel It can be seen that the agreement between the two modelsat frequencies below resonance is excellent In fact within the accuracy of the com-puter the predictions are identical if f lt 1

2f1 Combining equations (24) and (26)

the thickness of the layer is related to the reregection coemacrcient by

h =raquoc2

ordmfz 0

micro

R2

1 iexcl R2

para

(27)

From (27) it can be seen that as R approaches unity so the calculated thicknessapproaches inshynity In practical measurement this means that the spring approachloses accuracy as the reregection coemacrcient approaches unity The authors have foundthat for practical purposes R lt 09 gives satisfactory results

Proc R Soc Lond A (2003)

962 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

12

10

08

06

04

02

0 10 20 30 40 50

f (MHz)

refl

ecti

on c

oeff

icie

nt

spring model

continuum model

Figure 3 Comparison between spring-model and continuum-model predictions for theredegection-coeplusmncient spectra from a mineral oil macrlm between two steel elements

3 Acoustic properties of a lubricant macrlm

To determine the thickness of a lubricant shylm using (27) it is necessary to knowboth the density of and the speed of sound through the lubricant The speed ofsound can readily be determined for oil in the bulk from a simple ToF measurementbetween a transducer and a regat reregector For the oil used in these experiments (ShellTurbo T68) the acoustic properties at 20 macrC are shown in table 1

This value is suitable for the analysis of ambient reguid wedges or low-pressurehydrodynamic lubricant shylms However in EHD shylms the lubricant is subjectedto pressures high enough to cause solidishycation and a signishycant change in physi-cal properties The speed of sound through oil under EHD conditions is thereforevery dinoterent to those in the bulk The speed of propagation of a longitudinal wavethrough a medium depends on the density raquo and the bulk modulus B accordingto (see for example Povey 1997)

c =

s

B

raquo (31)

Jacobson amp Vinet (1987) provide a model to determine the inreguence of pressureon the compression and bulk modulus of liquid lubricants They give an equation ofstate to describe the behaviour of the lubricant under pressure p

p =3B0

x2(1 iexcl x)esup2(1iexclx) (32)

and the bulk modulus under pressure is given by

B =B0

x2[2 + (sup2 iexcl 1)x iexcl sup2x2]esup2(1iexclx) (33)

where B0 is the bulk modulus at zero pressure sup2 is a lubricant-specishyc parameterand x is a function of the relative compression

x = 3

r

raquo0

raquop (34)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 963

Table 2 Details of the transducers used in this work

(The focal length and spot size (equation (55)) are determined for a centre-frequency wave inwater)

bandwidth focal length spot sizecentre frequency (iexcl6 dB points) element diameter (in water) (in water)

f (MHz) (MHz) D (mm) F (mm) df (mm)

10 417 127 76 921

25 1732 635 54 522

50 4075 635 25 121

where raquo0 is the density at zero pressure and raquop the density at pressure p These equa-tions are used for the oil both in its liquid state and after it undergoes solidishycationbut employing dinoterent values of sup2 and B0

Jacobson amp Vinet used a high-pressure chamber to measure the compression ofseveral liquid lubricants up to pressures of 22 GPa and determined the parametersfor (32) and (33) For mineral oils the bulk modulus increased from 1517 GPaat atmospheric pressure to 2030 GPa at EHD pressures while the density increasedby 2030 Therefore from (31) the speed of sound within an EHD contact is likelyto be some two to four times greater than that under ambient conditions

Unfortunately there are no test data available specishycally for the lubricant usedin these studies (Shell Turbo T68) However parameters from a similar base oil(extracted from Jacobson amp Vinet (1987)) have been used to determine the relation-ship between bulk modulus density change and pressure Table 1 shows the resultsof this analysis for two oil pressures the lower corresponding to that experienced inthe ball on regat apparatus and the higher to that in ball-bearing contact

4 Ultrasonic redegection measurement apparatus

An ultrasonic pulser-receiver (UPR) generates a high-voltage pulse that causes apiezoelectric transducer to be excited in mechanical resonance The transducer thenemits a broadband pulse of ultrasonic energy As can be seen in shygure 1 this ultra-sonic pulse propagates through the bearing shell is reregected from the lubricant layerand is received by the same transducer Measurements were made using focused ultra-sonic transducers with a range of dinoterent centre frequencies (10 25 and 50 MHz)The transducers were immersed in a water bath and positioned so that the ultrasonicenergy was focused through the water bath and bearing shell onto the lubricant layerTable 2 details the bandwidth geometry and focusing properties of the transducersused

The pulse reregected from the lubricant layer was amplishyed and stored on a dig-ital oscilloscope The stored reregected signals were passed to a PC for processingFigure 4 shows a schematic of the apparatus and data signals Software (written inthe LabView environment) was written to control the UPR receive reregection signalsfrom the oscilloscope perform the required signal processing and display the requiredresults

Proc R Soc Lond A (2003)

964 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

ball bearing

raceway

focusedultrasonictransducer

lubricant film

controlsignal

digital scope

downloadwaveform to PC

UPR

PC

Figure 4 Schematic of ultrasonic pulsing and receiving system

transducer

water tank

shim

glasssheets

positioning scale

Figure 5 Schematic of the apparatus used for generatingthin liquid macrlms between two degat surfaces

5 Measurement of a stationary liquid layer

Initial experiments were performed on thin liquid layers between stationary solidsurfaces Two conshygurations were chosen a water wedge between optical glass regatsand an oil shylm between two eccentric cylinders The former apparatus was used toproduce a wide range of measurable liquid-layer thickness The latter was designed toinvestigate the enotects of the curvature of the solid surfaces and the use of a mineraloil as the liquid medium

(a) Liquid-wedge apparatus

Shims of various thickness were used to separate sheets of regoat glass which werethen immersed in a water tank as shown in shygure 5 The ultrasonic transducerswere also immersed in the water tank and mounted above the liquid wedge on acomputer-controlled xy positioning frame The ultrasonic pulsing and receiving wascontrolled by the apparatus as shown in shygure 4

The shyrst step in the procedure was to determine the frequency characteristics of theincident ultrasonic pulse The bottom glass plate was removed and the pulse reregected

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 965

6 7 8 9 10 11

10

09

08

07

06

05

04

03

02

refl

ect

ion c

oef

fici

ent

18 mm

53 mm

89 mm

124 mm

159 mm

195 mm

(a)

10

08

06

04

02

0

refl

ect

ion c

oeff

icie

nt

15 17 19 21 23 25 27 29 31 33

f (MHz)

125 mm 375 mm 50 mm 625 mm 75 mm(b)

Figure 6 Measured redegection-coeplusmncient spectra for a range of deguid macrlm thicknesses using(a) a 10 MHz and (b) a 25 MHz centre-frequency transducer

from the glasswater interface recorded This time-domain signal was converted tothe frequency domain via a fast Fourier transform and stored as a reference Aref Inthis way

Aref(f) = I(f)Rgw (51)

where I(f ) is the frequency-response characteristic of the incident pulse and Rgw

is the glasswater reregection coemacrcient given by (21) The bottom plate was thenrepositioned and measurements of the pulse reregected from the reguid shylm were recordedat various locations along the reguid wedge This measurement signal Am eas can bewritten as

Am eas (f) = I(f)Rl(f) (52)

Proc R Soc Lond A (2003)

966 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

25

20

15

10

5

0

film

thic

knes

s (m

m)

60 65 70 75 80 85 90 95 100 105 110

f (MHz)

Figure 7 Film-thickness results determined by the application ofthe spring model to the redegection spectra of macrgure 6a

where Rl(f) is the reregection-coemacrcient spectrum of the lubricant layer which canthen be obtained by combining (51) and (52)

Rl(f) =Am eas (f)

Aref(f)Rgw (53)

Figure 6 shows two sets of reregection-coemacrcient spectra of liquid layers in a liquid-wedge experiment recorded using two dinoterent wide-band transducers for a rangeof shylm thickness The thickness of the liquid layer at any measuring location wasestimated from the geometry of the reguid wedge formed by the shim

From shygure 6b it can be seen that at higher shylm thicknesses resonant frequencies(observed as minima in the reregection-coemacrcient spectra) are visible When these res-onances occur the layer thickness can be readily determined from (23) For thinnerliquid layers andor when using lower-frequency transducers the resonance is notobserved as it occurs beyond the frequency range of the transducer However theshape of the reregection-coemacrcient spectrum below resonance can be used to predictthe thickness of the liquid layer though the application of the spring model (equa-tion (27))

The stinotness of the layer can be measured over a range of frequencies with onetransducer As the stinotness at a single frequency is sumacrcient to enable prediction ofthe reguid-layer thickness there is some redundancy in the data that can be used as amethod of checking the accuracy of the spring model Figure 7 shows the data given inshygure 6a converted to shylm thickness via (27) over the bandwidth of the transducerFrom shygure 7 it can be seen that for the lower shylm-thickness values the curvesare horizontal This indicates a good measurement as the shylm thickness cannot bea function of the frequency with which it is measured However for the top curvethe model does not correctly convert the reregection coemacrcient to a constant layerthickness This is because as the reregection coemacrcient tends to unity so the springmodel (equation (27)) becomes prone to numerical error For the next curve down

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 967

0

10

20

30

40

50

70

mea

sure

d f

ilm

thic

kness

(m

m)

60

predicted film thickness (mm)

10 20 30 40 50 60 70

Figure 8 Film-thickness values measured by ultrasonic redegection compared withpredictions of the thickness determined from the geometry of the deguid wedge

at the higher frequencies the same happens This represents a limit of the spring-model approach and to measure these thicker shylms either lower frequencies shouldbe used so R is lower or higher frequencies used and the location of resonancesdetermined

Figure 8 shows ultrasonic measurements of the thickness of the liquid shylm com-pared with the geometrical prediction of the layer thickness The data below 25 mmcorrespond to measurements performed using the spring model while the data above25 mm have been determined from the measurement of shylm resonances Agreementis good (and a straight line is observed) but in practice the measured liquid-layerthickness tends to be slightly larger than that of the shim This is likely to becaused by either some thin residual of water between the shim of the glass plateor by deformation of the shim where it has been cut Each of these enotects wouldtend to make the liquid layer thicker and hence explain the dinoterence seen in shyg-ure 8

(b) Annular oil-macrlm apparatus

Figure 9 shows the apparatus to create an oil wedge between a ring and a shaft Thering and shaft were made from aluminium The ringshaft interface had a nominaldiameter of 70 mm and a diametral clearance of 100 mm The shaft was spring loadedagainst the ring By changing the position of the loading point the gap thicknessin the region above the transducer could be varied The gap was shylled with mineraloil (Shell Turbo T68) through a small shyller hole A 25 MHz focused transducer waslocated in a water bath beneath the assembly The transducer was positioned so thatthe wave was focused on the reguid layer

Figure 10 shows a plot of the shylm thickness determined from the reregection mea-surements for various angular positions of the loading point relative to the ultra-sonic measurement position In this case all the shylms were measured using theshylm-resonance method The theoretical width of annular gap h between eccentriccylinders is obtained from geometry

h = R1

middot

1 iexcl

micro

R1 iexcl R2

R1

para2

sin2 iquest

cedil1=2

iexcl R2 + (R1 iexcl R2) cos iquest (54)

Proc R Soc Lond A (2003)

968 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

transducer

water tank

measurement zone

oil-filled annulus

tension spring

aluminium cylinders

Figure 9 Apparatus used to create an annular oil macrlm for ultrasonic-redegection experiments

film

thic

knes

s (m

m)

100

90

80

70

60

50

40

30

20

10

0

angular position (deg)

-180 -135 -90 -45 0 45 90 135 180

ultrasonic measurements

mathematical solution

Figure 10 Film-thickness values measured by ultrasonic redegection for an annular macrlm betweentwo eccentric cylinders Experimental results are compared with the geometrical solution

where R1 and R2 are the radii of the bush and shaft respectively and rsquo is theangle measured from the point of contact Equation (54) is included in shygure 10 forcomparison and a good correlation was observed

To reduce the enotects of the curvature of the lubricated interface the transducersused in this experiment focus the wave onto the oil layer The spot size of the focusedwave varies with frequency according to the relationship (Silk 1984)

df(iexcl6 d B) =1028F c

fD (55)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 969

steel disc water bath

oil meniscus

rotating steel ball

transducer

hydraulic load

motor drive

Figure 11 Schematic of the experimental apparatus used to generatean EHD macrlm for a ball sliding on a degat

where df is the diameter of the spot size (where the signal has reduced to iexcl6 dBof its peak value) F is the transducer focusing length f is the wave frequencyc is the speed of sound in water and D is the diameter of the piezoelectric elementFor a 25 MHz frequency wave this corresponds to a spot size in water of 522 mmThis is small compared with the radius of the shaftbush apparatus So essentiallythe transducer is receiving signals back from a regat region of constant shylm thick-ness and the curvature has little enotect The good agreement between experimen-tal and theoretical liquid-layer thickness shown in shygure 10 further validates thishypothesis

6 Measurement of dynamic lubricating macrlms

An EHD lubricant shylm forms between rolling or sliding non-conformal contactsTypically the thickness of the oil layer is in the region of 011 mm This is withinthe range of the possible measurement by ultrasonic means and within the spring-model regime of ultrasonic response In this work EHD shylms have been measuredin a model rig containing a single stationary lubricated contact and in a rolling-element bearing where the lubricant shylm is transient (with respect to the trans-ducer)

(a) Ball on disc EHD lubrication apparatus

Figure 11 shows the apparatus used to generate a single EHD lubricated contactA steel ball is supported on rollers and hydraulically loaded onto the underside ofa steel disc The ball is rotated at constant speed by an electric motor througha gear box and quill shaft The steel disc is held stationary such that the ball iscompletely sliding against the underside of the disc This apparatus is a modishyed`optical elastohydrodynamicrsquo apparatus (originally developed by Cameron amp Gohar(1966)) where the semi-reregective rotating glass disc has been replaced by a station-

Proc R Soc Lond A (2003)

970 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

005

010

015

020

025

030

035

040

0 02 04 06 08 10 12 14

lubri

can

t fi

lm thic

kness

(m

m)

entrainment speed (m s-1)

theoretical solution a = 015 mmmeasurements a = 015 mmtheoretical solution a = 01 mmmeasurements a = 01 mm

Figure 12 EHD lubricant-macrlm-thickness variation with ball-sliding speed for two loadsUltrasonic-redegection measurements are compared with a theoretical solution

ary steel disc and the microscope replaced by an ultrasonic transducer The balldisc contact was regooded with a mineral oil (Shell Turbo T68) which is entrainedinto the contact to form an EHD shylm A 50 MHz focused transducer was mountedabove the contact in a water bath The transducer was positioned directly abovethe contact region and at a distance such that the wave is focused on the balldiscinterface

Reregected pulses were recorded from the discball interface as the ball rotationalspeed and load were varied A reference spectrum was obtained by recording the pulsereregected when the ball was out of contact with the disc but the disc was still regoodedwith oil As in the wedge experiment the reference and lubricant-layer measurementswere used in (32) to obtain the reregection-coemacrcient spectrum of the lubricant layerA series of reregection coemacrcient spectra were then recorded from the discball contactas the sliding speed was increased The spring model (equation (27)) was used todetermine the shylm thickness from these spectra An automated LabView interfacewas written to record the spectra divide by a reference and convert the data intoshylm thickness (as shown in shygure 6) As discussed in x 3 above the density and speedof sound of the oil used in (27) are those at contact pressure (in this case 08 GPa)and not those in the bulk

Figure 12 shows the measured variation in shylm thickness determined from thereregection coemacrcient spectra as the speed is increased for two load cases (giving con-tact radii a of 01 and 015 mm) For this lubrication case a theoretical predictionof the oil-shylm thickness can be obtained from the regression equations of Dowson ampHigginson (1966) The central shylm thickness hc is expressed as a regression equationconsisting of shyve non-dimensional parameters

Hc = 269U 067G053W iexcl0067(1 iexcl 061eiexcl073k) (61)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 971

test rolling bearing

measurement zone

hydraulic loading

focusing transducer

water bath

belt and pulley drive

Figure 13 Schematic of apparatus used for ultrasonic measurementsof macrlm thickness in rolling-element bearings

where

Hc =hc

Rx

W =P

2EcurrenR2x

U =sup20u

2EcurrenRx

k = 103

micro

Ry

Rx

para064

G = 2notEcurren

where Ecurren is the reduced modulus Rx and Ry are the reduced radii in the paralleland transverse directions u is the mean surface speed P is the applied contact loadsup20 is the viscosity of oil in the inlet and not is its pressure-viscosity coemacrcient

The predictions of (61) for the two load cases are plotted in shygure 12 The agree-ment between the theoretical solution and the experimental data is good Typicallythe measured data are repeatable to within sect20 The oil shylm generated by theapparatus is not completely stable To directly observe the lubricant shylm the steeldisc was replaced by the glass disc and the shylm monitored visually A certain amountof shylm reguctuation was observed during normal running (caused by a slight processingof the ball on its supporting rollers) Notwithstanding the results are encouragingbecause this indicates that both the integrity of the ultrasonic method and alsothat the speed of sound of the lubricating oil compares well with predictions fromhigh-pressure measurements

(b) Rolling bearing lubricant-macrlm measurement

The duration of the ultrasonic pulses used in this work was short Spatially thepulse width was typically three wavelengths in length A 25 MHz wave travelling insteel results in a pulse duration of 01 ms Therefore it is feasible to record the shylmthickness in a rolling element moving past the focal point of an ultrasonic transducer

The approach has been used to measure shylm thickness in a 6410 deep-grooveball bearing Figure 13 shows a schematic of the bearing and the positioning of thetransducer The 25 MHz transducer (see table 2 for details) was located in a small

Proc R Soc Lond A (2003)

972 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

0

01

02

03

04

05

07

01 02 03 04 05 06 07

theo

reti

cal

film

thic

knes

s pre

dic

tion (

mm

)

45 kN 112 RPM 60 kN 72 RPM

60 kN 103 RPM 60 kN 128 RPM

60 kN 135 RPM 60 kN 137 RPM

60 kN 178 RPM 60 kN 195 RPM

60 kN 297 RPM 60 kN 375 RPM

75 kN 48 RPM 75 kN 124 RPM

06

measured film thickness (mm)

Figure 14 Comparison of rolling-element-bearing macrlm thickness measured byan ultrasonic means with EHD theoretical solution

water bath machined out of the bearing bush The transducer was spherically focusedand positioned in the water bath so that the wave was focused on the contact betweena ball and the raceway The bearing was loaded hydraulically and rotated by anelectric motor The bearing cavity was regooded with a mineral oil (Shell Turbo T68) Athermocouple was positioned on the outer raceway near the ultrasonic measurementpoint The bearing was loaded to give a contact eclipse between the ball and theouter raceway of semi-major and semi-minor axes 115 and 08 mm respectivelyThe bearing was then rotated and the transducer set to continuously pulse at arepetition rate of 10 kHz

The focal spot size of the transducer was ca 500 mm The maximum rotationalspeed of the bearing in these tests was 375 rpm At this rotational speed theregion of focused ultrasound would remain completely within the lubricated con-tact for ca 05 ms This allowed approximately shyve discrete pulses of ultrasound tobe reregected from the lubricant shylm as each ball passed through the measurementzone Initially a reference reregected pulse was recorded when the bearing was station-ary and there was no ball located over the measurement zone (although the cavitywas still shylled with oil) If a pulse is incident on an EHD shylm its amplitude is reducedbecause part of the wave has been transmitted through the oil shylm into the ball Bycontinuously monitoring the signals reregected from the raceway measurements of theball-raceway contacts were made Of the shyve pulses reregected from the ball-racewaycontact the lowest amplitude pulse was selected for analysis This pulse correspondsto the thinnest measured shylm thickness It should be noted that the resolution of thefocused transducer and the measurement interval are such that it was not possibleto record the horseshoe-shaped minimum shylm-thickness constriction at the contactexit The selected pulse was analysed shyrstly using (53) to calculate the reregection

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 973

film

thic

knes

s (m

m)

1000

100

10

1

01

001

00010 10 20 30 40 50 60

f (MHz)

time of flight limit

resonance method limit

spring model upper limit (R = 09)

spring model lower limit (R = 01)

Figure 15 Limits of operation for macrlm-thickness measurement by ultrasonic means

coemacrcient and then using the spring model to predict the shylm thickness The speedof sound in the oil in the contact is set to c = 4400 m siexcl1 (determined using themethod described in x 3)

Figure 14 shows the measured shylm thickness plotted against a prediction of theshylm thickness from the solution for an elliptical contact of Dowson amp Higginson(1966) (equation (61)) The bearing and lubricant heats up during operation Thetemperature of the entrained oil was monitored and used to determine an appropriateviscosity with which to calculate the shylm thickness in (61) This was why the resultswere not plotted as shylm thickness against speed (as in shygure 11) because viscositywas varying throughout the test

The results in shygure 14 show good agreement between measured lubricant-shylmthickness and that predicted by the EHD regression equations The spread along thex-axis shows the variation in shylm for nominally the same bearing operating conditions(load speed and oil temperature) At this stage it is not clear whether this scatteris a result of the measurement process or whether this is the actual shylm thicknessin the bearing It is worth noting that this measurement process could be improvedif the exact position of the ball could be related to the ultrasonic measurement soallowing a more precise measurement of the minimum shylm thickness

7 Discussion limits of operation

It is instructive to consider the limits of shylm-thickness measurement for a given ultra-sonic frequency The simplest method for determining the thickness of a lubricantlayer providing it is sumacrciently thick is by measuring the ToF through the layerA reregection occurs at the layer front face and another at the back face The thick-ness is readily obtained from the time between the arrival of these pulses multipliedby the acoustic velocity For the method to work the two reregected pulses must besumacrciently discrete and so the propagation distance must be greater than the pulse

Proc R Soc Lond A (2003)

974 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

width and so the minimum shylm thickness detectable by this method is given by

h gtnc

2f (71)

where n is the number of wavelengths in the ultrasonic pulse typically around threeThis measurement limit is plotted in shygure 15 as the minimum frequency requiredto measure a given shylm thickness Conventional ultrasonic non-destructive testingis generally restricted by losses in the propagating media (steel in this case) tofrequencies below 4060 MHz From (71) this means that the ToF method is onlypractically useful for layers of thickness greater than 40 mm This is thicker than thatfound on most commercial bearing systems

A lubricant layer resonates at a frequency given by (23) This equation also givesthe low thickness limit for this technique as the upper frequency output by a giventransducer determined the lowest measurable layer thickness This limit is also shownin shygure 15 for the shyrst through-thickness mode (ie m = 1) So using the highestpractical frequencies shylms greater than 10 mm are measurable by the shylm-resonancemethod

The upper limit of shylm thickness measurable using the spring-model approach isreached as R tends to unity in (27) Experience shows that measurements of R lessthan 09 yield satisfactory results The lowest shylm thickness measurable will dependon the smallest possible value of R This in turn will depend on the signal-to-noiseratio A signal-to-noise ratio of 60 dB is typical for conventional ultrasonic non-destructive testing systems The noise amplitude is thus 1

1000of the pulse amplitude

In the case of a measurement on a real bearing the achievable signal-to-noise ratiowill be reduced by the transducer-bearing reregection coemacrcient and by the attenuationin the bearing shell This means that the pulse incident in the reguid shylm will bereduced from that output by the transducer by a factor of shyve (as a conservativeestimate) Further it is assumed that for reliable measurements a pulse reregectedfrom the oil layer should have an amplitude approximately 20 times that of the noiselevel This results in a minimum measurable reregection coemacrcient of R = 01 Therelationships between the shylm thickness and the transducer frequency for the upperlimit when R = 09 and the lower where R = 01 are shown in shygure 15

This indicates that for a measuring frequency of 60 MHz a lubricant shylm of 2 nmis measurable This opens up the possibility of measuring boundary-type lubricantshylms between machine elements However the models presented here are designedfor a parallel-sided oil layer completely separating the smooth bearing surface If atthese low shylm thickness metal-to-metal contact occurs then transmission will occurat this location In this case some alternative method for interpreting reregectioncoemacrcients will be needed

8 Conclusions

Ultrasound is reregected from the lubricant shylm between bearing surfaces It is possibleto deduce the thickness of the lubricant shylm by comparing the frequency spectrumof the reregected pulse with that of the incident pulse The response of the lubricantlayer to an ultrasonic pulse has been modelled using both a spring-model methodand a continuum method The spring model is suitable for thin lubricant shylms inwhich the wavelength of the ultrasound is much larger than the layer thickness The

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 975

continuum model is valid for all layer thicknesses and allows the prediction of thethrough-thickness resonant frequencies of the lubricant layers Measurement of thesethrough-thickness resonances also provides a means of measuring the layer thickness

Experiments on reguid layers between regat plates and eccentric rings have demon-strated that ultrasound can suitably measure a wide range of liquid layer thicknessThe EHD lubricant shylm that forms between a ball sliding on a regat surface hasalso been measured ultrasonically The measured results agree well with theoreti-cal predictions taking into account the greatly increased speed of sound throughthe lubricant when it is under high pressure Films in the range 50500 nm wererecorded

The approach can also be used to measure shylm thickness in a rolling-elementbearing An ultrasonic transducer was mounted on the bearing raceway and thepulse reregected from the lubricant layer generated as the ball passes was recordedAgain measured results agreed well with theoretical predictions

The lower limit of measurement by this method depends on the signal-to-noiseratio A continuum model showed that using frequencies up to 60 MHz permits themeasurement of 2 nm thick shylms There is no upper limit to shylm-thickness measure-ment Thick shylms (greater than 40 mm) can be measured by a time-of-regight methodFilms of intermediate thickness can be determined by measuring the frequency atwhich the shylm resonates

This work was funded by a grant from the UK Engineering and Physical Sciences ResearchCouncil under the ROPA programme The authors acknowledge the help of Phil Harper of theUniversity of Sheplusmneld for his assistance with some of the measurements

References

Astridge D G amp Longmacreld M D 1967 Capacitance measurement and oil macrlm thickness in alarge radius disc and ring machine Proc Inst Mech Engrs 182 8996

Cameron A amp Gohar R 1966 Theoretical and experimental studies of the oil macrlm in lubricatedpoint contact Proc R Soc Lond A 291 520536

Dowson D amp Higginson G R 1966 Elastohydrodynamic lubrication|the fundamentals of roller

and gear lubrication Oxford Pergamon

Drinkwater B W Dwyer-Joyce R S amp Cawley P 1996 A study of the interaction betweenultrasound and a partially contacting solidsolid interface Proc R Soc Lond A 452 26132628

El-Sisi S I amp Shawki G S A 1960 Measurement of oil-macrlm thickness between disks by electricalconductivity Trans ASME J Basic Engng 82 12

Hamilton G M amp Moore S L 1967 A modimacred gauge for investigating an elastohydrodynamiccontact Proc Inst Mech Engrs 182 251

Hamrock B J 1994 Fundamentals of deguid macrlm lubrication McGraw-Hill

Hosten B 1991 Bulk heterogeneous plane-wave propagation through viscoelastic plates andstratimacred media with large values of frequency-domain Ultrasonics 29 445450

Jacobson B O amp Vinet P 1987 A model for the indeguence of pressure on the bulk modulusand the indeguence of temperature on the solidimacrcation pressure for liquid lubricants Trans

ASME J Tribology 109 709

Johnston G J Wayte R amp Spikes H A 1991 The measurement and study of very thinlubricant macrlms in concentrated contacts Tribol Trans 34 187194

Kinra V K Jaminet P T Zhu C amp Iyer V R 1994 Simultaneous measurement of theacoustical properties of a thin-layered medium the inverse problem J Acoust Soc Am 9530593074

Proc R Soc Lond A (2003)

960 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

20 mm 15 mm

1 mm

01 mm

12

10

08

06

04

02

0 20 30 40 50 6010

f (MHz)

refl

ect

ion c

oeff

icie

nt

Figure 2 Continuum-model predictions of the redegection-coeplusmncient spectrumfrom a layer of mineral oil between two steel elements

Table 1 Acoustic properties of lubricating oil (Shell Turbo T68) at room temperature and

ambient and EHD pressures (estimated using the method of Jacobson amp Vinet (1987 ))

(Also included for comparison water and steel properties)

density bulk modulus wave velocityraquo (kg m iexcl 3) B (GPa) c (m s iexcl 1 )

oil at atmospheric pressure 876 184 1450

oil at 08 GPa 1002 126 3550

oil at 15 GPa 1044 212 4500

water at atmospheric pressure 1000 206 1483

steel 7923 172 5840

tem these models can be used to predict the reregection and transmission of planewaves through a given system Figure 2 shows a continuum-model prediction of thereregection coemacrcient spectrum for 01 10 15 and 20 mm thickness mineral oil layersbetween two steel half-spaces The material properties used in this calculation areshown in table 1 This is essentially the impulse response function of the systemie it gives the response of the system for an incident wave of unit amplitude In shyg-ure 2 the resonant frequencies are seen as sharp minima in the reregection-coemacrcientspectrum The minima seen at 363 MHz corresponds to a lubricant-shylm thicknessof 20 mm

Pialucha et al (1989) used a continuum-model approach to show that the reso-nant frequencies of an embedded layer are related to its thickness h and acousticproperties by

h =cm

2fm (23)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 961

where c is the speed of sound in the lubricant layer m is the mode number of theresonant frequency and fm is the resonant frequency (in Hz) of the mth mode It canbe seen from consideration of (23) that higher resonant frequencies correspond tothinner lubricant shylms The thinnest shylm measurable by this approach is then limitedby the upper operating frequency In practice the frequency is limited to below 4060 MHz by the attenuation of the ultrasonic pulse in the bearing materials Thismeans that if the lubricant layer is below 10 mm the resonant frequency will beabove the measurable range

The region below the shyrst resonance of a simple mass-spring system is known asthe stinotness-controlled region because the deregection of the mass is dependent purelyon the applied load and the spring stinotness In the same way it can be shown (Hosten1991) that the interaction of ultrasound with a very thin layer (which would havea very high shyrst resonant frequency) is governed by the stinotness of that layer Thestinotness per unit area K of a thin layer is given by

K =raquoc2

h (24)

where raquo is the density of the layer and c the speed of sound in the layer This springstinotness can then be used in a quasi-static model of the interaction of ultrasound withthe lubricant layer In this way Tattersall (1973) demonstrated that the reregectioncoemacrcient of the layer was given by the expression

R =z1 iexcl z2 + i(z1z2=K)

z1 + z2 + i(z1z2=K) (25)

where z1 and z2 refer to the acoustic impedance of the materials either side of thelubricant layer For identical materials either side of the lubricant shylm (z1 = z2 = z 0)this reduces to

R =1

p

1 + (K=ordmfz0) (26)

Drinkwater et al (1996) used the above analysis to determine the stinotness of drycontacts in which the interface between two rough surfaces composed of air gapsand regions of asperity contact acts like a layer of reduced stinotness Measurementof the reregection coemacrcient and hence interface stinotness can give information aboutthe degree of conformity of the contacting surfaces

Figure 3 shows a comparison between the spring-model prediction and thecontinuum-model prediction for the reregection-coemacrcient spectra from a mineral oillayer surrounded by steel It can be seen that the agreement between the two modelsat frequencies below resonance is excellent In fact within the accuracy of the com-puter the predictions are identical if f lt 1

2f1 Combining equations (24) and (26)

the thickness of the layer is related to the reregection coemacrcient by

h =raquoc2

ordmfz 0

micro

R2

1 iexcl R2

para

(27)

From (27) it can be seen that as R approaches unity so the calculated thicknessapproaches inshynity In practical measurement this means that the spring approachloses accuracy as the reregection coemacrcient approaches unity The authors have foundthat for practical purposes R lt 09 gives satisfactory results

Proc R Soc Lond A (2003)

962 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

12

10

08

06

04

02

0 10 20 30 40 50

f (MHz)

refl

ecti

on c

oeff

icie

nt

spring model

continuum model

Figure 3 Comparison between spring-model and continuum-model predictions for theredegection-coeplusmncient spectra from a mineral oil macrlm between two steel elements

3 Acoustic properties of a lubricant macrlm

To determine the thickness of a lubricant shylm using (27) it is necessary to knowboth the density of and the speed of sound through the lubricant The speed ofsound can readily be determined for oil in the bulk from a simple ToF measurementbetween a transducer and a regat reregector For the oil used in these experiments (ShellTurbo T68) the acoustic properties at 20 macrC are shown in table 1

This value is suitable for the analysis of ambient reguid wedges or low-pressurehydrodynamic lubricant shylms However in EHD shylms the lubricant is subjectedto pressures high enough to cause solidishycation and a signishycant change in physi-cal properties The speed of sound through oil under EHD conditions is thereforevery dinoterent to those in the bulk The speed of propagation of a longitudinal wavethrough a medium depends on the density raquo and the bulk modulus B accordingto (see for example Povey 1997)

c =

s

B

raquo (31)

Jacobson amp Vinet (1987) provide a model to determine the inreguence of pressureon the compression and bulk modulus of liquid lubricants They give an equation ofstate to describe the behaviour of the lubricant under pressure p

p =3B0

x2(1 iexcl x)esup2(1iexclx) (32)

and the bulk modulus under pressure is given by

B =B0

x2[2 + (sup2 iexcl 1)x iexcl sup2x2]esup2(1iexclx) (33)

where B0 is the bulk modulus at zero pressure sup2 is a lubricant-specishyc parameterand x is a function of the relative compression

x = 3

r

raquo0

raquop (34)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 963

Table 2 Details of the transducers used in this work

(The focal length and spot size (equation (55)) are determined for a centre-frequency wave inwater)

bandwidth focal length spot sizecentre frequency (iexcl6 dB points) element diameter (in water) (in water)

f (MHz) (MHz) D (mm) F (mm) df (mm)

10 417 127 76 921

25 1732 635 54 522

50 4075 635 25 121

where raquo0 is the density at zero pressure and raquop the density at pressure p These equa-tions are used for the oil both in its liquid state and after it undergoes solidishycationbut employing dinoterent values of sup2 and B0

Jacobson amp Vinet used a high-pressure chamber to measure the compression ofseveral liquid lubricants up to pressures of 22 GPa and determined the parametersfor (32) and (33) For mineral oils the bulk modulus increased from 1517 GPaat atmospheric pressure to 2030 GPa at EHD pressures while the density increasedby 2030 Therefore from (31) the speed of sound within an EHD contact is likelyto be some two to four times greater than that under ambient conditions

Unfortunately there are no test data available specishycally for the lubricant usedin these studies (Shell Turbo T68) However parameters from a similar base oil(extracted from Jacobson amp Vinet (1987)) have been used to determine the relation-ship between bulk modulus density change and pressure Table 1 shows the resultsof this analysis for two oil pressures the lower corresponding to that experienced inthe ball on regat apparatus and the higher to that in ball-bearing contact

4 Ultrasonic redegection measurement apparatus

An ultrasonic pulser-receiver (UPR) generates a high-voltage pulse that causes apiezoelectric transducer to be excited in mechanical resonance The transducer thenemits a broadband pulse of ultrasonic energy As can be seen in shygure 1 this ultra-sonic pulse propagates through the bearing shell is reregected from the lubricant layerand is received by the same transducer Measurements were made using focused ultra-sonic transducers with a range of dinoterent centre frequencies (10 25 and 50 MHz)The transducers were immersed in a water bath and positioned so that the ultrasonicenergy was focused through the water bath and bearing shell onto the lubricant layerTable 2 details the bandwidth geometry and focusing properties of the transducersused

The pulse reregected from the lubricant layer was amplishyed and stored on a dig-ital oscilloscope The stored reregected signals were passed to a PC for processingFigure 4 shows a schematic of the apparatus and data signals Software (written inthe LabView environment) was written to control the UPR receive reregection signalsfrom the oscilloscope perform the required signal processing and display the requiredresults

Proc R Soc Lond A (2003)

964 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

ball bearing

raceway

focusedultrasonictransducer

lubricant film

controlsignal

digital scope

downloadwaveform to PC

UPR

PC

Figure 4 Schematic of ultrasonic pulsing and receiving system

transducer

water tank

shim

glasssheets

positioning scale

Figure 5 Schematic of the apparatus used for generatingthin liquid macrlms between two degat surfaces

5 Measurement of a stationary liquid layer

Initial experiments were performed on thin liquid layers between stationary solidsurfaces Two conshygurations were chosen a water wedge between optical glass regatsand an oil shylm between two eccentric cylinders The former apparatus was used toproduce a wide range of measurable liquid-layer thickness The latter was designed toinvestigate the enotects of the curvature of the solid surfaces and the use of a mineraloil as the liquid medium

(a) Liquid-wedge apparatus

Shims of various thickness were used to separate sheets of regoat glass which werethen immersed in a water tank as shown in shygure 5 The ultrasonic transducerswere also immersed in the water tank and mounted above the liquid wedge on acomputer-controlled xy positioning frame The ultrasonic pulsing and receiving wascontrolled by the apparatus as shown in shygure 4

The shyrst step in the procedure was to determine the frequency characteristics of theincident ultrasonic pulse The bottom glass plate was removed and the pulse reregected

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 965

6 7 8 9 10 11

10

09

08

07

06

05

04

03

02

refl

ect

ion c

oef

fici

ent

18 mm

53 mm

89 mm

124 mm

159 mm

195 mm

(a)

10

08

06

04

02

0

refl

ect

ion c

oeff

icie

nt

15 17 19 21 23 25 27 29 31 33

f (MHz)

125 mm 375 mm 50 mm 625 mm 75 mm(b)

Figure 6 Measured redegection-coeplusmncient spectra for a range of deguid macrlm thicknesses using(a) a 10 MHz and (b) a 25 MHz centre-frequency transducer

from the glasswater interface recorded This time-domain signal was converted tothe frequency domain via a fast Fourier transform and stored as a reference Aref Inthis way

Aref(f) = I(f)Rgw (51)

where I(f ) is the frequency-response characteristic of the incident pulse and Rgw

is the glasswater reregection coemacrcient given by (21) The bottom plate was thenrepositioned and measurements of the pulse reregected from the reguid shylm were recordedat various locations along the reguid wedge This measurement signal Am eas can bewritten as

Am eas (f) = I(f)Rl(f) (52)

Proc R Soc Lond A (2003)

966 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

25

20

15

10

5

0

film

thic

knes

s (m

m)

60 65 70 75 80 85 90 95 100 105 110

f (MHz)

Figure 7 Film-thickness results determined by the application ofthe spring model to the redegection spectra of macrgure 6a

where Rl(f) is the reregection-coemacrcient spectrum of the lubricant layer which canthen be obtained by combining (51) and (52)

Rl(f) =Am eas (f)

Aref(f)Rgw (53)

Figure 6 shows two sets of reregection-coemacrcient spectra of liquid layers in a liquid-wedge experiment recorded using two dinoterent wide-band transducers for a rangeof shylm thickness The thickness of the liquid layer at any measuring location wasestimated from the geometry of the reguid wedge formed by the shim

From shygure 6b it can be seen that at higher shylm thicknesses resonant frequencies(observed as minima in the reregection-coemacrcient spectra) are visible When these res-onances occur the layer thickness can be readily determined from (23) For thinnerliquid layers andor when using lower-frequency transducers the resonance is notobserved as it occurs beyond the frequency range of the transducer However theshape of the reregection-coemacrcient spectrum below resonance can be used to predictthe thickness of the liquid layer though the application of the spring model (equa-tion (27))

The stinotness of the layer can be measured over a range of frequencies with onetransducer As the stinotness at a single frequency is sumacrcient to enable prediction ofthe reguid-layer thickness there is some redundancy in the data that can be used as amethod of checking the accuracy of the spring model Figure 7 shows the data given inshygure 6a converted to shylm thickness via (27) over the bandwidth of the transducerFrom shygure 7 it can be seen that for the lower shylm-thickness values the curvesare horizontal This indicates a good measurement as the shylm thickness cannot bea function of the frequency with which it is measured However for the top curvethe model does not correctly convert the reregection coemacrcient to a constant layerthickness This is because as the reregection coemacrcient tends to unity so the springmodel (equation (27)) becomes prone to numerical error For the next curve down

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 967

0

10

20

30

40

50

70

mea

sure

d f

ilm

thic

kness

(m

m)

60

predicted film thickness (mm)

10 20 30 40 50 60 70

Figure 8 Film-thickness values measured by ultrasonic redegection compared withpredictions of the thickness determined from the geometry of the deguid wedge

at the higher frequencies the same happens This represents a limit of the spring-model approach and to measure these thicker shylms either lower frequencies shouldbe used so R is lower or higher frequencies used and the location of resonancesdetermined

Figure 8 shows ultrasonic measurements of the thickness of the liquid shylm com-pared with the geometrical prediction of the layer thickness The data below 25 mmcorrespond to measurements performed using the spring model while the data above25 mm have been determined from the measurement of shylm resonances Agreementis good (and a straight line is observed) but in practice the measured liquid-layerthickness tends to be slightly larger than that of the shim This is likely to becaused by either some thin residual of water between the shim of the glass plateor by deformation of the shim where it has been cut Each of these enotects wouldtend to make the liquid layer thicker and hence explain the dinoterence seen in shyg-ure 8

(b) Annular oil-macrlm apparatus

Figure 9 shows the apparatus to create an oil wedge between a ring and a shaft Thering and shaft were made from aluminium The ringshaft interface had a nominaldiameter of 70 mm and a diametral clearance of 100 mm The shaft was spring loadedagainst the ring By changing the position of the loading point the gap thicknessin the region above the transducer could be varied The gap was shylled with mineraloil (Shell Turbo T68) through a small shyller hole A 25 MHz focused transducer waslocated in a water bath beneath the assembly The transducer was positioned so thatthe wave was focused on the reguid layer

Figure 10 shows a plot of the shylm thickness determined from the reregection mea-surements for various angular positions of the loading point relative to the ultra-sonic measurement position In this case all the shylms were measured using theshylm-resonance method The theoretical width of annular gap h between eccentriccylinders is obtained from geometry

h = R1

middot

1 iexcl

micro

R1 iexcl R2

R1

para2

sin2 iquest

cedil1=2

iexcl R2 + (R1 iexcl R2) cos iquest (54)

Proc R Soc Lond A (2003)

968 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

transducer

water tank

measurement zone

oil-filled annulus

tension spring

aluminium cylinders

Figure 9 Apparatus used to create an annular oil macrlm for ultrasonic-redegection experiments

film

thic

knes

s (m

m)

100

90

80

70

60

50

40

30

20

10

0

angular position (deg)

-180 -135 -90 -45 0 45 90 135 180

ultrasonic measurements

mathematical solution

Figure 10 Film-thickness values measured by ultrasonic redegection for an annular macrlm betweentwo eccentric cylinders Experimental results are compared with the geometrical solution

where R1 and R2 are the radii of the bush and shaft respectively and rsquo is theangle measured from the point of contact Equation (54) is included in shygure 10 forcomparison and a good correlation was observed

To reduce the enotects of the curvature of the lubricated interface the transducersused in this experiment focus the wave onto the oil layer The spot size of the focusedwave varies with frequency according to the relationship (Silk 1984)

df(iexcl6 d B) =1028F c

fD (55)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 969

steel disc water bath

oil meniscus

rotating steel ball

transducer

hydraulic load

motor drive

Figure 11 Schematic of the experimental apparatus used to generatean EHD macrlm for a ball sliding on a degat

where df is the diameter of the spot size (where the signal has reduced to iexcl6 dBof its peak value) F is the transducer focusing length f is the wave frequencyc is the speed of sound in water and D is the diameter of the piezoelectric elementFor a 25 MHz frequency wave this corresponds to a spot size in water of 522 mmThis is small compared with the radius of the shaftbush apparatus So essentiallythe transducer is receiving signals back from a regat region of constant shylm thick-ness and the curvature has little enotect The good agreement between experimen-tal and theoretical liquid-layer thickness shown in shygure 10 further validates thishypothesis

6 Measurement of dynamic lubricating macrlms

An EHD lubricant shylm forms between rolling or sliding non-conformal contactsTypically the thickness of the oil layer is in the region of 011 mm This is withinthe range of the possible measurement by ultrasonic means and within the spring-model regime of ultrasonic response In this work EHD shylms have been measuredin a model rig containing a single stationary lubricated contact and in a rolling-element bearing where the lubricant shylm is transient (with respect to the trans-ducer)

(a) Ball on disc EHD lubrication apparatus

Figure 11 shows the apparatus used to generate a single EHD lubricated contactA steel ball is supported on rollers and hydraulically loaded onto the underside ofa steel disc The ball is rotated at constant speed by an electric motor througha gear box and quill shaft The steel disc is held stationary such that the ball iscompletely sliding against the underside of the disc This apparatus is a modishyed`optical elastohydrodynamicrsquo apparatus (originally developed by Cameron amp Gohar(1966)) where the semi-reregective rotating glass disc has been replaced by a station-

Proc R Soc Lond A (2003)

970 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

005

010

015

020

025

030

035

040

0 02 04 06 08 10 12 14

lubri

can

t fi

lm thic

kness

(m

m)

entrainment speed (m s-1)

theoretical solution a = 015 mmmeasurements a = 015 mmtheoretical solution a = 01 mmmeasurements a = 01 mm

Figure 12 EHD lubricant-macrlm-thickness variation with ball-sliding speed for two loadsUltrasonic-redegection measurements are compared with a theoretical solution

ary steel disc and the microscope replaced by an ultrasonic transducer The balldisc contact was regooded with a mineral oil (Shell Turbo T68) which is entrainedinto the contact to form an EHD shylm A 50 MHz focused transducer was mountedabove the contact in a water bath The transducer was positioned directly abovethe contact region and at a distance such that the wave is focused on the balldiscinterface

Reregected pulses were recorded from the discball interface as the ball rotationalspeed and load were varied A reference spectrum was obtained by recording the pulsereregected when the ball was out of contact with the disc but the disc was still regoodedwith oil As in the wedge experiment the reference and lubricant-layer measurementswere used in (32) to obtain the reregection-coemacrcient spectrum of the lubricant layerA series of reregection coemacrcient spectra were then recorded from the discball contactas the sliding speed was increased The spring model (equation (27)) was used todetermine the shylm thickness from these spectra An automated LabView interfacewas written to record the spectra divide by a reference and convert the data intoshylm thickness (as shown in shygure 6) As discussed in x 3 above the density and speedof sound of the oil used in (27) are those at contact pressure (in this case 08 GPa)and not those in the bulk

Figure 12 shows the measured variation in shylm thickness determined from thereregection coemacrcient spectra as the speed is increased for two load cases (giving con-tact radii a of 01 and 015 mm) For this lubrication case a theoretical predictionof the oil-shylm thickness can be obtained from the regression equations of Dowson ampHigginson (1966) The central shylm thickness hc is expressed as a regression equationconsisting of shyve non-dimensional parameters

Hc = 269U 067G053W iexcl0067(1 iexcl 061eiexcl073k) (61)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 971

test rolling bearing

measurement zone

hydraulic loading

focusing transducer

water bath

belt and pulley drive

Figure 13 Schematic of apparatus used for ultrasonic measurementsof macrlm thickness in rolling-element bearings

where

Hc =hc

Rx

W =P

2EcurrenR2x

U =sup20u

2EcurrenRx

k = 103

micro

Ry

Rx

para064

G = 2notEcurren

where Ecurren is the reduced modulus Rx and Ry are the reduced radii in the paralleland transverse directions u is the mean surface speed P is the applied contact loadsup20 is the viscosity of oil in the inlet and not is its pressure-viscosity coemacrcient

The predictions of (61) for the two load cases are plotted in shygure 12 The agree-ment between the theoretical solution and the experimental data is good Typicallythe measured data are repeatable to within sect20 The oil shylm generated by theapparatus is not completely stable To directly observe the lubricant shylm the steeldisc was replaced by the glass disc and the shylm monitored visually A certain amountof shylm reguctuation was observed during normal running (caused by a slight processingof the ball on its supporting rollers) Notwithstanding the results are encouragingbecause this indicates that both the integrity of the ultrasonic method and alsothat the speed of sound of the lubricating oil compares well with predictions fromhigh-pressure measurements

(b) Rolling bearing lubricant-macrlm measurement

The duration of the ultrasonic pulses used in this work was short Spatially thepulse width was typically three wavelengths in length A 25 MHz wave travelling insteel results in a pulse duration of 01 ms Therefore it is feasible to record the shylmthickness in a rolling element moving past the focal point of an ultrasonic transducer

The approach has been used to measure shylm thickness in a 6410 deep-grooveball bearing Figure 13 shows a schematic of the bearing and the positioning of thetransducer The 25 MHz transducer (see table 2 for details) was located in a small

Proc R Soc Lond A (2003)

972 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

0

01

02

03

04

05

07

01 02 03 04 05 06 07

theo

reti

cal

film

thic

knes

s pre

dic

tion (

mm

)

45 kN 112 RPM 60 kN 72 RPM

60 kN 103 RPM 60 kN 128 RPM

60 kN 135 RPM 60 kN 137 RPM

60 kN 178 RPM 60 kN 195 RPM

60 kN 297 RPM 60 kN 375 RPM

75 kN 48 RPM 75 kN 124 RPM

06

measured film thickness (mm)

Figure 14 Comparison of rolling-element-bearing macrlm thickness measured byan ultrasonic means with EHD theoretical solution

water bath machined out of the bearing bush The transducer was spherically focusedand positioned in the water bath so that the wave was focused on the contact betweena ball and the raceway The bearing was loaded hydraulically and rotated by anelectric motor The bearing cavity was regooded with a mineral oil (Shell Turbo T68) Athermocouple was positioned on the outer raceway near the ultrasonic measurementpoint The bearing was loaded to give a contact eclipse between the ball and theouter raceway of semi-major and semi-minor axes 115 and 08 mm respectivelyThe bearing was then rotated and the transducer set to continuously pulse at arepetition rate of 10 kHz

The focal spot size of the transducer was ca 500 mm The maximum rotationalspeed of the bearing in these tests was 375 rpm At this rotational speed theregion of focused ultrasound would remain completely within the lubricated con-tact for ca 05 ms This allowed approximately shyve discrete pulses of ultrasound tobe reregected from the lubricant shylm as each ball passed through the measurementzone Initially a reference reregected pulse was recorded when the bearing was station-ary and there was no ball located over the measurement zone (although the cavitywas still shylled with oil) If a pulse is incident on an EHD shylm its amplitude is reducedbecause part of the wave has been transmitted through the oil shylm into the ball Bycontinuously monitoring the signals reregected from the raceway measurements of theball-raceway contacts were made Of the shyve pulses reregected from the ball-racewaycontact the lowest amplitude pulse was selected for analysis This pulse correspondsto the thinnest measured shylm thickness It should be noted that the resolution of thefocused transducer and the measurement interval are such that it was not possibleto record the horseshoe-shaped minimum shylm-thickness constriction at the contactexit The selected pulse was analysed shyrstly using (53) to calculate the reregection

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 973

film

thic

knes

s (m

m)

1000

100

10

1

01

001

00010 10 20 30 40 50 60

f (MHz)

time of flight limit

resonance method limit

spring model upper limit (R = 09)

spring model lower limit (R = 01)

Figure 15 Limits of operation for macrlm-thickness measurement by ultrasonic means

coemacrcient and then using the spring model to predict the shylm thickness The speedof sound in the oil in the contact is set to c = 4400 m siexcl1 (determined using themethod described in x 3)

Figure 14 shows the measured shylm thickness plotted against a prediction of theshylm thickness from the solution for an elliptical contact of Dowson amp Higginson(1966) (equation (61)) The bearing and lubricant heats up during operation Thetemperature of the entrained oil was monitored and used to determine an appropriateviscosity with which to calculate the shylm thickness in (61) This was why the resultswere not plotted as shylm thickness against speed (as in shygure 11) because viscositywas varying throughout the test

The results in shygure 14 show good agreement between measured lubricant-shylmthickness and that predicted by the EHD regression equations The spread along thex-axis shows the variation in shylm for nominally the same bearing operating conditions(load speed and oil temperature) At this stage it is not clear whether this scatteris a result of the measurement process or whether this is the actual shylm thicknessin the bearing It is worth noting that this measurement process could be improvedif the exact position of the ball could be related to the ultrasonic measurement soallowing a more precise measurement of the minimum shylm thickness

7 Discussion limits of operation

It is instructive to consider the limits of shylm-thickness measurement for a given ultra-sonic frequency The simplest method for determining the thickness of a lubricantlayer providing it is sumacrciently thick is by measuring the ToF through the layerA reregection occurs at the layer front face and another at the back face The thick-ness is readily obtained from the time between the arrival of these pulses multipliedby the acoustic velocity For the method to work the two reregected pulses must besumacrciently discrete and so the propagation distance must be greater than the pulse

Proc R Soc Lond A (2003)

974 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

width and so the minimum shylm thickness detectable by this method is given by

h gtnc

2f (71)

where n is the number of wavelengths in the ultrasonic pulse typically around threeThis measurement limit is plotted in shygure 15 as the minimum frequency requiredto measure a given shylm thickness Conventional ultrasonic non-destructive testingis generally restricted by losses in the propagating media (steel in this case) tofrequencies below 4060 MHz From (71) this means that the ToF method is onlypractically useful for layers of thickness greater than 40 mm This is thicker than thatfound on most commercial bearing systems

A lubricant layer resonates at a frequency given by (23) This equation also givesthe low thickness limit for this technique as the upper frequency output by a giventransducer determined the lowest measurable layer thickness This limit is also shownin shygure 15 for the shyrst through-thickness mode (ie m = 1) So using the highestpractical frequencies shylms greater than 10 mm are measurable by the shylm-resonancemethod

The upper limit of shylm thickness measurable using the spring-model approach isreached as R tends to unity in (27) Experience shows that measurements of R lessthan 09 yield satisfactory results The lowest shylm thickness measurable will dependon the smallest possible value of R This in turn will depend on the signal-to-noiseratio A signal-to-noise ratio of 60 dB is typical for conventional ultrasonic non-destructive testing systems The noise amplitude is thus 1

1000of the pulse amplitude

In the case of a measurement on a real bearing the achievable signal-to-noise ratiowill be reduced by the transducer-bearing reregection coemacrcient and by the attenuationin the bearing shell This means that the pulse incident in the reguid shylm will bereduced from that output by the transducer by a factor of shyve (as a conservativeestimate) Further it is assumed that for reliable measurements a pulse reregectedfrom the oil layer should have an amplitude approximately 20 times that of the noiselevel This results in a minimum measurable reregection coemacrcient of R = 01 Therelationships between the shylm thickness and the transducer frequency for the upperlimit when R = 09 and the lower where R = 01 are shown in shygure 15

This indicates that for a measuring frequency of 60 MHz a lubricant shylm of 2 nmis measurable This opens up the possibility of measuring boundary-type lubricantshylms between machine elements However the models presented here are designedfor a parallel-sided oil layer completely separating the smooth bearing surface If atthese low shylm thickness metal-to-metal contact occurs then transmission will occurat this location In this case some alternative method for interpreting reregectioncoemacrcients will be needed

8 Conclusions

Ultrasound is reregected from the lubricant shylm between bearing surfaces It is possibleto deduce the thickness of the lubricant shylm by comparing the frequency spectrumof the reregected pulse with that of the incident pulse The response of the lubricantlayer to an ultrasonic pulse has been modelled using both a spring-model methodand a continuum method The spring model is suitable for thin lubricant shylms inwhich the wavelength of the ultrasound is much larger than the layer thickness The

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 975

continuum model is valid for all layer thicknesses and allows the prediction of thethrough-thickness resonant frequencies of the lubricant layers Measurement of thesethrough-thickness resonances also provides a means of measuring the layer thickness

Experiments on reguid layers between regat plates and eccentric rings have demon-strated that ultrasound can suitably measure a wide range of liquid layer thicknessThe EHD lubricant shylm that forms between a ball sliding on a regat surface hasalso been measured ultrasonically The measured results agree well with theoreti-cal predictions taking into account the greatly increased speed of sound throughthe lubricant when it is under high pressure Films in the range 50500 nm wererecorded

The approach can also be used to measure shylm thickness in a rolling-elementbearing An ultrasonic transducer was mounted on the bearing raceway and thepulse reregected from the lubricant layer generated as the ball passes was recordedAgain measured results agreed well with theoretical predictions

The lower limit of measurement by this method depends on the signal-to-noiseratio A continuum model showed that using frequencies up to 60 MHz permits themeasurement of 2 nm thick shylms There is no upper limit to shylm-thickness measure-ment Thick shylms (greater than 40 mm) can be measured by a time-of-regight methodFilms of intermediate thickness can be determined by measuring the frequency atwhich the shylm resonates

This work was funded by a grant from the UK Engineering and Physical Sciences ResearchCouncil under the ROPA programme The authors acknowledge the help of Phil Harper of theUniversity of Sheplusmneld for his assistance with some of the measurements

References

Astridge D G amp Longmacreld M D 1967 Capacitance measurement and oil macrlm thickness in alarge radius disc and ring machine Proc Inst Mech Engrs 182 8996

Cameron A amp Gohar R 1966 Theoretical and experimental studies of the oil macrlm in lubricatedpoint contact Proc R Soc Lond A 291 520536

Dowson D amp Higginson G R 1966 Elastohydrodynamic lubrication|the fundamentals of roller

and gear lubrication Oxford Pergamon

Drinkwater B W Dwyer-Joyce R S amp Cawley P 1996 A study of the interaction betweenultrasound and a partially contacting solidsolid interface Proc R Soc Lond A 452 26132628

El-Sisi S I amp Shawki G S A 1960 Measurement of oil-macrlm thickness between disks by electricalconductivity Trans ASME J Basic Engng 82 12

Hamilton G M amp Moore S L 1967 A modimacred gauge for investigating an elastohydrodynamiccontact Proc Inst Mech Engrs 182 251

Hamrock B J 1994 Fundamentals of deguid macrlm lubrication McGraw-Hill

Hosten B 1991 Bulk heterogeneous plane-wave propagation through viscoelastic plates andstratimacred media with large values of frequency-domain Ultrasonics 29 445450

Jacobson B O amp Vinet P 1987 A model for the indeguence of pressure on the bulk modulusand the indeguence of temperature on the solidimacrcation pressure for liquid lubricants Trans

ASME J Tribology 109 709

Johnston G J Wayte R amp Spikes H A 1991 The measurement and study of very thinlubricant macrlms in concentrated contacts Tribol Trans 34 187194

Kinra V K Jaminet P T Zhu C amp Iyer V R 1994 Simultaneous measurement of theacoustical properties of a thin-layered medium the inverse problem J Acoust Soc Am 9530593074

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 961

where c is the speed of sound in the lubricant layer m is the mode number of theresonant frequency and fm is the resonant frequency (in Hz) of the mth mode It canbe seen from consideration of (23) that higher resonant frequencies correspond tothinner lubricant shylms The thinnest shylm measurable by this approach is then limitedby the upper operating frequency In practice the frequency is limited to below 4060 MHz by the attenuation of the ultrasonic pulse in the bearing materials Thismeans that if the lubricant layer is below 10 mm the resonant frequency will beabove the measurable range

The region below the shyrst resonance of a simple mass-spring system is known asthe stinotness-controlled region because the deregection of the mass is dependent purelyon the applied load and the spring stinotness In the same way it can be shown (Hosten1991) that the interaction of ultrasound with a very thin layer (which would havea very high shyrst resonant frequency) is governed by the stinotness of that layer Thestinotness per unit area K of a thin layer is given by

K =raquoc2

h (24)

where raquo is the density of the layer and c the speed of sound in the layer This springstinotness can then be used in a quasi-static model of the interaction of ultrasound withthe lubricant layer In this way Tattersall (1973) demonstrated that the reregectioncoemacrcient of the layer was given by the expression

R =z1 iexcl z2 + i(z1z2=K)

z1 + z2 + i(z1z2=K) (25)

where z1 and z2 refer to the acoustic impedance of the materials either side of thelubricant layer For identical materials either side of the lubricant shylm (z1 = z2 = z 0)this reduces to

R =1

p

1 + (K=ordmfz0) (26)

Drinkwater et al (1996) used the above analysis to determine the stinotness of drycontacts in which the interface between two rough surfaces composed of air gapsand regions of asperity contact acts like a layer of reduced stinotness Measurementof the reregection coemacrcient and hence interface stinotness can give information aboutthe degree of conformity of the contacting surfaces

Figure 3 shows a comparison between the spring-model prediction and thecontinuum-model prediction for the reregection-coemacrcient spectra from a mineral oillayer surrounded by steel It can be seen that the agreement between the two modelsat frequencies below resonance is excellent In fact within the accuracy of the com-puter the predictions are identical if f lt 1

2f1 Combining equations (24) and (26)

the thickness of the layer is related to the reregection coemacrcient by

h =raquoc2

ordmfz 0

micro

R2

1 iexcl R2

para

(27)

From (27) it can be seen that as R approaches unity so the calculated thicknessapproaches inshynity In practical measurement this means that the spring approachloses accuracy as the reregection coemacrcient approaches unity The authors have foundthat for practical purposes R lt 09 gives satisfactory results

Proc R Soc Lond A (2003)

962 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

12

10

08

06

04

02

0 10 20 30 40 50

f (MHz)

refl

ecti

on c

oeff

icie

nt

spring model

continuum model

Figure 3 Comparison between spring-model and continuum-model predictions for theredegection-coeplusmncient spectra from a mineral oil macrlm between two steel elements

3 Acoustic properties of a lubricant macrlm

To determine the thickness of a lubricant shylm using (27) it is necessary to knowboth the density of and the speed of sound through the lubricant The speed ofsound can readily be determined for oil in the bulk from a simple ToF measurementbetween a transducer and a regat reregector For the oil used in these experiments (ShellTurbo T68) the acoustic properties at 20 macrC are shown in table 1

This value is suitable for the analysis of ambient reguid wedges or low-pressurehydrodynamic lubricant shylms However in EHD shylms the lubricant is subjectedto pressures high enough to cause solidishycation and a signishycant change in physi-cal properties The speed of sound through oil under EHD conditions is thereforevery dinoterent to those in the bulk The speed of propagation of a longitudinal wavethrough a medium depends on the density raquo and the bulk modulus B accordingto (see for example Povey 1997)

c =

s

B

raquo (31)

Jacobson amp Vinet (1987) provide a model to determine the inreguence of pressureon the compression and bulk modulus of liquid lubricants They give an equation ofstate to describe the behaviour of the lubricant under pressure p

p =3B0

x2(1 iexcl x)esup2(1iexclx) (32)

and the bulk modulus under pressure is given by

B =B0

x2[2 + (sup2 iexcl 1)x iexcl sup2x2]esup2(1iexclx) (33)

where B0 is the bulk modulus at zero pressure sup2 is a lubricant-specishyc parameterand x is a function of the relative compression

x = 3

r

raquo0

raquop (34)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 963

Table 2 Details of the transducers used in this work

(The focal length and spot size (equation (55)) are determined for a centre-frequency wave inwater)

bandwidth focal length spot sizecentre frequency (iexcl6 dB points) element diameter (in water) (in water)

f (MHz) (MHz) D (mm) F (mm) df (mm)

10 417 127 76 921

25 1732 635 54 522

50 4075 635 25 121

where raquo0 is the density at zero pressure and raquop the density at pressure p These equa-tions are used for the oil both in its liquid state and after it undergoes solidishycationbut employing dinoterent values of sup2 and B0

Jacobson amp Vinet used a high-pressure chamber to measure the compression ofseveral liquid lubricants up to pressures of 22 GPa and determined the parametersfor (32) and (33) For mineral oils the bulk modulus increased from 1517 GPaat atmospheric pressure to 2030 GPa at EHD pressures while the density increasedby 2030 Therefore from (31) the speed of sound within an EHD contact is likelyto be some two to four times greater than that under ambient conditions

Unfortunately there are no test data available specishycally for the lubricant usedin these studies (Shell Turbo T68) However parameters from a similar base oil(extracted from Jacobson amp Vinet (1987)) have been used to determine the relation-ship between bulk modulus density change and pressure Table 1 shows the resultsof this analysis for two oil pressures the lower corresponding to that experienced inthe ball on regat apparatus and the higher to that in ball-bearing contact

4 Ultrasonic redegection measurement apparatus

An ultrasonic pulser-receiver (UPR) generates a high-voltage pulse that causes apiezoelectric transducer to be excited in mechanical resonance The transducer thenemits a broadband pulse of ultrasonic energy As can be seen in shygure 1 this ultra-sonic pulse propagates through the bearing shell is reregected from the lubricant layerand is received by the same transducer Measurements were made using focused ultra-sonic transducers with a range of dinoterent centre frequencies (10 25 and 50 MHz)The transducers were immersed in a water bath and positioned so that the ultrasonicenergy was focused through the water bath and bearing shell onto the lubricant layerTable 2 details the bandwidth geometry and focusing properties of the transducersused

The pulse reregected from the lubricant layer was amplishyed and stored on a dig-ital oscilloscope The stored reregected signals were passed to a PC for processingFigure 4 shows a schematic of the apparatus and data signals Software (written inthe LabView environment) was written to control the UPR receive reregection signalsfrom the oscilloscope perform the required signal processing and display the requiredresults

Proc R Soc Lond A (2003)

964 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

ball bearing

raceway

focusedultrasonictransducer

lubricant film

controlsignal

digital scope

downloadwaveform to PC

UPR

PC

Figure 4 Schematic of ultrasonic pulsing and receiving system

transducer

water tank

shim

glasssheets

positioning scale

Figure 5 Schematic of the apparatus used for generatingthin liquid macrlms between two degat surfaces

5 Measurement of a stationary liquid layer

Initial experiments were performed on thin liquid layers between stationary solidsurfaces Two conshygurations were chosen a water wedge between optical glass regatsand an oil shylm between two eccentric cylinders The former apparatus was used toproduce a wide range of measurable liquid-layer thickness The latter was designed toinvestigate the enotects of the curvature of the solid surfaces and the use of a mineraloil as the liquid medium

(a) Liquid-wedge apparatus

Shims of various thickness were used to separate sheets of regoat glass which werethen immersed in a water tank as shown in shygure 5 The ultrasonic transducerswere also immersed in the water tank and mounted above the liquid wedge on acomputer-controlled xy positioning frame The ultrasonic pulsing and receiving wascontrolled by the apparatus as shown in shygure 4

The shyrst step in the procedure was to determine the frequency characteristics of theincident ultrasonic pulse The bottom glass plate was removed and the pulse reregected

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 965

6 7 8 9 10 11

10

09

08

07

06

05

04

03

02

refl

ect

ion c

oef

fici

ent

18 mm

53 mm

89 mm

124 mm

159 mm

195 mm

(a)

10

08

06

04

02

0

refl

ect

ion c

oeff

icie

nt

15 17 19 21 23 25 27 29 31 33

f (MHz)

125 mm 375 mm 50 mm 625 mm 75 mm(b)

Figure 6 Measured redegection-coeplusmncient spectra for a range of deguid macrlm thicknesses using(a) a 10 MHz and (b) a 25 MHz centre-frequency transducer

from the glasswater interface recorded This time-domain signal was converted tothe frequency domain via a fast Fourier transform and stored as a reference Aref Inthis way

Aref(f) = I(f)Rgw (51)

where I(f ) is the frequency-response characteristic of the incident pulse and Rgw

is the glasswater reregection coemacrcient given by (21) The bottom plate was thenrepositioned and measurements of the pulse reregected from the reguid shylm were recordedat various locations along the reguid wedge This measurement signal Am eas can bewritten as

Am eas (f) = I(f)Rl(f) (52)

Proc R Soc Lond A (2003)

966 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

25

20

15

10

5

0

film

thic

knes

s (m

m)

60 65 70 75 80 85 90 95 100 105 110

f (MHz)

Figure 7 Film-thickness results determined by the application ofthe spring model to the redegection spectra of macrgure 6a

where Rl(f) is the reregection-coemacrcient spectrum of the lubricant layer which canthen be obtained by combining (51) and (52)

Rl(f) =Am eas (f)

Aref(f)Rgw (53)

Figure 6 shows two sets of reregection-coemacrcient spectra of liquid layers in a liquid-wedge experiment recorded using two dinoterent wide-band transducers for a rangeof shylm thickness The thickness of the liquid layer at any measuring location wasestimated from the geometry of the reguid wedge formed by the shim

From shygure 6b it can be seen that at higher shylm thicknesses resonant frequencies(observed as minima in the reregection-coemacrcient spectra) are visible When these res-onances occur the layer thickness can be readily determined from (23) For thinnerliquid layers andor when using lower-frequency transducers the resonance is notobserved as it occurs beyond the frequency range of the transducer However theshape of the reregection-coemacrcient spectrum below resonance can be used to predictthe thickness of the liquid layer though the application of the spring model (equa-tion (27))

The stinotness of the layer can be measured over a range of frequencies with onetransducer As the stinotness at a single frequency is sumacrcient to enable prediction ofthe reguid-layer thickness there is some redundancy in the data that can be used as amethod of checking the accuracy of the spring model Figure 7 shows the data given inshygure 6a converted to shylm thickness via (27) over the bandwidth of the transducerFrom shygure 7 it can be seen that for the lower shylm-thickness values the curvesare horizontal This indicates a good measurement as the shylm thickness cannot bea function of the frequency with which it is measured However for the top curvethe model does not correctly convert the reregection coemacrcient to a constant layerthickness This is because as the reregection coemacrcient tends to unity so the springmodel (equation (27)) becomes prone to numerical error For the next curve down

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 967

0

10

20

30

40

50

70

mea

sure

d f

ilm

thic

kness

(m

m)

60

predicted film thickness (mm)

10 20 30 40 50 60 70

Figure 8 Film-thickness values measured by ultrasonic redegection compared withpredictions of the thickness determined from the geometry of the deguid wedge

at the higher frequencies the same happens This represents a limit of the spring-model approach and to measure these thicker shylms either lower frequencies shouldbe used so R is lower or higher frequencies used and the location of resonancesdetermined

Figure 8 shows ultrasonic measurements of the thickness of the liquid shylm com-pared with the geometrical prediction of the layer thickness The data below 25 mmcorrespond to measurements performed using the spring model while the data above25 mm have been determined from the measurement of shylm resonances Agreementis good (and a straight line is observed) but in practice the measured liquid-layerthickness tends to be slightly larger than that of the shim This is likely to becaused by either some thin residual of water between the shim of the glass plateor by deformation of the shim where it has been cut Each of these enotects wouldtend to make the liquid layer thicker and hence explain the dinoterence seen in shyg-ure 8

(b) Annular oil-macrlm apparatus

Figure 9 shows the apparatus to create an oil wedge between a ring and a shaft Thering and shaft were made from aluminium The ringshaft interface had a nominaldiameter of 70 mm and a diametral clearance of 100 mm The shaft was spring loadedagainst the ring By changing the position of the loading point the gap thicknessin the region above the transducer could be varied The gap was shylled with mineraloil (Shell Turbo T68) through a small shyller hole A 25 MHz focused transducer waslocated in a water bath beneath the assembly The transducer was positioned so thatthe wave was focused on the reguid layer

Figure 10 shows a plot of the shylm thickness determined from the reregection mea-surements for various angular positions of the loading point relative to the ultra-sonic measurement position In this case all the shylms were measured using theshylm-resonance method The theoretical width of annular gap h between eccentriccylinders is obtained from geometry

h = R1

middot

1 iexcl

micro

R1 iexcl R2

R1

para2

sin2 iquest

cedil1=2

iexcl R2 + (R1 iexcl R2) cos iquest (54)

Proc R Soc Lond A (2003)

968 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

transducer

water tank

measurement zone

oil-filled annulus

tension spring

aluminium cylinders

Figure 9 Apparatus used to create an annular oil macrlm for ultrasonic-redegection experiments

film

thic

knes

s (m

m)

100

90

80

70

60

50

40

30

20

10

0

angular position (deg)

-180 -135 -90 -45 0 45 90 135 180

ultrasonic measurements

mathematical solution

Figure 10 Film-thickness values measured by ultrasonic redegection for an annular macrlm betweentwo eccentric cylinders Experimental results are compared with the geometrical solution

where R1 and R2 are the radii of the bush and shaft respectively and rsquo is theangle measured from the point of contact Equation (54) is included in shygure 10 forcomparison and a good correlation was observed

To reduce the enotects of the curvature of the lubricated interface the transducersused in this experiment focus the wave onto the oil layer The spot size of the focusedwave varies with frequency according to the relationship (Silk 1984)

df(iexcl6 d B) =1028F c

fD (55)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 969

steel disc water bath

oil meniscus

rotating steel ball

transducer

hydraulic load

motor drive

Figure 11 Schematic of the experimental apparatus used to generatean EHD macrlm for a ball sliding on a degat

where df is the diameter of the spot size (where the signal has reduced to iexcl6 dBof its peak value) F is the transducer focusing length f is the wave frequencyc is the speed of sound in water and D is the diameter of the piezoelectric elementFor a 25 MHz frequency wave this corresponds to a spot size in water of 522 mmThis is small compared with the radius of the shaftbush apparatus So essentiallythe transducer is receiving signals back from a regat region of constant shylm thick-ness and the curvature has little enotect The good agreement between experimen-tal and theoretical liquid-layer thickness shown in shygure 10 further validates thishypothesis

6 Measurement of dynamic lubricating macrlms

An EHD lubricant shylm forms between rolling or sliding non-conformal contactsTypically the thickness of the oil layer is in the region of 011 mm This is withinthe range of the possible measurement by ultrasonic means and within the spring-model regime of ultrasonic response In this work EHD shylms have been measuredin a model rig containing a single stationary lubricated contact and in a rolling-element bearing where the lubricant shylm is transient (with respect to the trans-ducer)

(a) Ball on disc EHD lubrication apparatus

Figure 11 shows the apparatus used to generate a single EHD lubricated contactA steel ball is supported on rollers and hydraulically loaded onto the underside ofa steel disc The ball is rotated at constant speed by an electric motor througha gear box and quill shaft The steel disc is held stationary such that the ball iscompletely sliding against the underside of the disc This apparatus is a modishyed`optical elastohydrodynamicrsquo apparatus (originally developed by Cameron amp Gohar(1966)) where the semi-reregective rotating glass disc has been replaced by a station-

Proc R Soc Lond A (2003)

970 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

005

010

015

020

025

030

035

040

0 02 04 06 08 10 12 14

lubri

can

t fi

lm thic

kness

(m

m)

entrainment speed (m s-1)

theoretical solution a = 015 mmmeasurements a = 015 mmtheoretical solution a = 01 mmmeasurements a = 01 mm

Figure 12 EHD lubricant-macrlm-thickness variation with ball-sliding speed for two loadsUltrasonic-redegection measurements are compared with a theoretical solution

ary steel disc and the microscope replaced by an ultrasonic transducer The balldisc contact was regooded with a mineral oil (Shell Turbo T68) which is entrainedinto the contact to form an EHD shylm A 50 MHz focused transducer was mountedabove the contact in a water bath The transducer was positioned directly abovethe contact region and at a distance such that the wave is focused on the balldiscinterface

Reregected pulses were recorded from the discball interface as the ball rotationalspeed and load were varied A reference spectrum was obtained by recording the pulsereregected when the ball was out of contact with the disc but the disc was still regoodedwith oil As in the wedge experiment the reference and lubricant-layer measurementswere used in (32) to obtain the reregection-coemacrcient spectrum of the lubricant layerA series of reregection coemacrcient spectra were then recorded from the discball contactas the sliding speed was increased The spring model (equation (27)) was used todetermine the shylm thickness from these spectra An automated LabView interfacewas written to record the spectra divide by a reference and convert the data intoshylm thickness (as shown in shygure 6) As discussed in x 3 above the density and speedof sound of the oil used in (27) are those at contact pressure (in this case 08 GPa)and not those in the bulk

Figure 12 shows the measured variation in shylm thickness determined from thereregection coemacrcient spectra as the speed is increased for two load cases (giving con-tact radii a of 01 and 015 mm) For this lubrication case a theoretical predictionof the oil-shylm thickness can be obtained from the regression equations of Dowson ampHigginson (1966) The central shylm thickness hc is expressed as a regression equationconsisting of shyve non-dimensional parameters

Hc = 269U 067G053W iexcl0067(1 iexcl 061eiexcl073k) (61)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 971

test rolling bearing

measurement zone

hydraulic loading

focusing transducer

water bath

belt and pulley drive

Figure 13 Schematic of apparatus used for ultrasonic measurementsof macrlm thickness in rolling-element bearings

where

Hc =hc

Rx

W =P

2EcurrenR2x

U =sup20u

2EcurrenRx

k = 103

micro

Ry

Rx

para064

G = 2notEcurren

where Ecurren is the reduced modulus Rx and Ry are the reduced radii in the paralleland transverse directions u is the mean surface speed P is the applied contact loadsup20 is the viscosity of oil in the inlet and not is its pressure-viscosity coemacrcient

The predictions of (61) for the two load cases are plotted in shygure 12 The agree-ment between the theoretical solution and the experimental data is good Typicallythe measured data are repeatable to within sect20 The oil shylm generated by theapparatus is not completely stable To directly observe the lubricant shylm the steeldisc was replaced by the glass disc and the shylm monitored visually A certain amountof shylm reguctuation was observed during normal running (caused by a slight processingof the ball on its supporting rollers) Notwithstanding the results are encouragingbecause this indicates that both the integrity of the ultrasonic method and alsothat the speed of sound of the lubricating oil compares well with predictions fromhigh-pressure measurements

(b) Rolling bearing lubricant-macrlm measurement

The duration of the ultrasonic pulses used in this work was short Spatially thepulse width was typically three wavelengths in length A 25 MHz wave travelling insteel results in a pulse duration of 01 ms Therefore it is feasible to record the shylmthickness in a rolling element moving past the focal point of an ultrasonic transducer

The approach has been used to measure shylm thickness in a 6410 deep-grooveball bearing Figure 13 shows a schematic of the bearing and the positioning of thetransducer The 25 MHz transducer (see table 2 for details) was located in a small

Proc R Soc Lond A (2003)

972 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

0

01

02

03

04

05

07

01 02 03 04 05 06 07

theo

reti

cal

film

thic

knes

s pre

dic

tion (

mm

)

45 kN 112 RPM 60 kN 72 RPM

60 kN 103 RPM 60 kN 128 RPM

60 kN 135 RPM 60 kN 137 RPM

60 kN 178 RPM 60 kN 195 RPM

60 kN 297 RPM 60 kN 375 RPM

75 kN 48 RPM 75 kN 124 RPM

06

measured film thickness (mm)

Figure 14 Comparison of rolling-element-bearing macrlm thickness measured byan ultrasonic means with EHD theoretical solution

water bath machined out of the bearing bush The transducer was spherically focusedand positioned in the water bath so that the wave was focused on the contact betweena ball and the raceway The bearing was loaded hydraulically and rotated by anelectric motor The bearing cavity was regooded with a mineral oil (Shell Turbo T68) Athermocouple was positioned on the outer raceway near the ultrasonic measurementpoint The bearing was loaded to give a contact eclipse between the ball and theouter raceway of semi-major and semi-minor axes 115 and 08 mm respectivelyThe bearing was then rotated and the transducer set to continuously pulse at arepetition rate of 10 kHz

The focal spot size of the transducer was ca 500 mm The maximum rotationalspeed of the bearing in these tests was 375 rpm At this rotational speed theregion of focused ultrasound would remain completely within the lubricated con-tact for ca 05 ms This allowed approximately shyve discrete pulses of ultrasound tobe reregected from the lubricant shylm as each ball passed through the measurementzone Initially a reference reregected pulse was recorded when the bearing was station-ary and there was no ball located over the measurement zone (although the cavitywas still shylled with oil) If a pulse is incident on an EHD shylm its amplitude is reducedbecause part of the wave has been transmitted through the oil shylm into the ball Bycontinuously monitoring the signals reregected from the raceway measurements of theball-raceway contacts were made Of the shyve pulses reregected from the ball-racewaycontact the lowest amplitude pulse was selected for analysis This pulse correspondsto the thinnest measured shylm thickness It should be noted that the resolution of thefocused transducer and the measurement interval are such that it was not possibleto record the horseshoe-shaped minimum shylm-thickness constriction at the contactexit The selected pulse was analysed shyrstly using (53) to calculate the reregection

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 973

film

thic

knes

s (m

m)

1000

100

10

1

01

001

00010 10 20 30 40 50 60

f (MHz)

time of flight limit

resonance method limit

spring model upper limit (R = 09)

spring model lower limit (R = 01)

Figure 15 Limits of operation for macrlm-thickness measurement by ultrasonic means

coemacrcient and then using the spring model to predict the shylm thickness The speedof sound in the oil in the contact is set to c = 4400 m siexcl1 (determined using themethod described in x 3)

Figure 14 shows the measured shylm thickness plotted against a prediction of theshylm thickness from the solution for an elliptical contact of Dowson amp Higginson(1966) (equation (61)) The bearing and lubricant heats up during operation Thetemperature of the entrained oil was monitored and used to determine an appropriateviscosity with which to calculate the shylm thickness in (61) This was why the resultswere not plotted as shylm thickness against speed (as in shygure 11) because viscositywas varying throughout the test

The results in shygure 14 show good agreement between measured lubricant-shylmthickness and that predicted by the EHD regression equations The spread along thex-axis shows the variation in shylm for nominally the same bearing operating conditions(load speed and oil temperature) At this stage it is not clear whether this scatteris a result of the measurement process or whether this is the actual shylm thicknessin the bearing It is worth noting that this measurement process could be improvedif the exact position of the ball could be related to the ultrasonic measurement soallowing a more precise measurement of the minimum shylm thickness

7 Discussion limits of operation

It is instructive to consider the limits of shylm-thickness measurement for a given ultra-sonic frequency The simplest method for determining the thickness of a lubricantlayer providing it is sumacrciently thick is by measuring the ToF through the layerA reregection occurs at the layer front face and another at the back face The thick-ness is readily obtained from the time between the arrival of these pulses multipliedby the acoustic velocity For the method to work the two reregected pulses must besumacrciently discrete and so the propagation distance must be greater than the pulse

Proc R Soc Lond A (2003)

974 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

width and so the minimum shylm thickness detectable by this method is given by

h gtnc

2f (71)

where n is the number of wavelengths in the ultrasonic pulse typically around threeThis measurement limit is plotted in shygure 15 as the minimum frequency requiredto measure a given shylm thickness Conventional ultrasonic non-destructive testingis generally restricted by losses in the propagating media (steel in this case) tofrequencies below 4060 MHz From (71) this means that the ToF method is onlypractically useful for layers of thickness greater than 40 mm This is thicker than thatfound on most commercial bearing systems

A lubricant layer resonates at a frequency given by (23) This equation also givesthe low thickness limit for this technique as the upper frequency output by a giventransducer determined the lowest measurable layer thickness This limit is also shownin shygure 15 for the shyrst through-thickness mode (ie m = 1) So using the highestpractical frequencies shylms greater than 10 mm are measurable by the shylm-resonancemethod

The upper limit of shylm thickness measurable using the spring-model approach isreached as R tends to unity in (27) Experience shows that measurements of R lessthan 09 yield satisfactory results The lowest shylm thickness measurable will dependon the smallest possible value of R This in turn will depend on the signal-to-noiseratio A signal-to-noise ratio of 60 dB is typical for conventional ultrasonic non-destructive testing systems The noise amplitude is thus 1

1000of the pulse amplitude

In the case of a measurement on a real bearing the achievable signal-to-noise ratiowill be reduced by the transducer-bearing reregection coemacrcient and by the attenuationin the bearing shell This means that the pulse incident in the reguid shylm will bereduced from that output by the transducer by a factor of shyve (as a conservativeestimate) Further it is assumed that for reliable measurements a pulse reregectedfrom the oil layer should have an amplitude approximately 20 times that of the noiselevel This results in a minimum measurable reregection coemacrcient of R = 01 Therelationships between the shylm thickness and the transducer frequency for the upperlimit when R = 09 and the lower where R = 01 are shown in shygure 15

This indicates that for a measuring frequency of 60 MHz a lubricant shylm of 2 nmis measurable This opens up the possibility of measuring boundary-type lubricantshylms between machine elements However the models presented here are designedfor a parallel-sided oil layer completely separating the smooth bearing surface If atthese low shylm thickness metal-to-metal contact occurs then transmission will occurat this location In this case some alternative method for interpreting reregectioncoemacrcients will be needed

8 Conclusions

Ultrasound is reregected from the lubricant shylm between bearing surfaces It is possibleto deduce the thickness of the lubricant shylm by comparing the frequency spectrumof the reregected pulse with that of the incident pulse The response of the lubricantlayer to an ultrasonic pulse has been modelled using both a spring-model methodand a continuum method The spring model is suitable for thin lubricant shylms inwhich the wavelength of the ultrasound is much larger than the layer thickness The

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 975

continuum model is valid for all layer thicknesses and allows the prediction of thethrough-thickness resonant frequencies of the lubricant layers Measurement of thesethrough-thickness resonances also provides a means of measuring the layer thickness

Experiments on reguid layers between regat plates and eccentric rings have demon-strated that ultrasound can suitably measure a wide range of liquid layer thicknessThe EHD lubricant shylm that forms between a ball sliding on a regat surface hasalso been measured ultrasonically The measured results agree well with theoreti-cal predictions taking into account the greatly increased speed of sound throughthe lubricant when it is under high pressure Films in the range 50500 nm wererecorded

The approach can also be used to measure shylm thickness in a rolling-elementbearing An ultrasonic transducer was mounted on the bearing raceway and thepulse reregected from the lubricant layer generated as the ball passes was recordedAgain measured results agreed well with theoretical predictions

The lower limit of measurement by this method depends on the signal-to-noiseratio A continuum model showed that using frequencies up to 60 MHz permits themeasurement of 2 nm thick shylms There is no upper limit to shylm-thickness measure-ment Thick shylms (greater than 40 mm) can be measured by a time-of-regight methodFilms of intermediate thickness can be determined by measuring the frequency atwhich the shylm resonates

This work was funded by a grant from the UK Engineering and Physical Sciences ResearchCouncil under the ROPA programme The authors acknowledge the help of Phil Harper of theUniversity of Sheplusmneld for his assistance with some of the measurements

References

Astridge D G amp Longmacreld M D 1967 Capacitance measurement and oil macrlm thickness in alarge radius disc and ring machine Proc Inst Mech Engrs 182 8996

Cameron A amp Gohar R 1966 Theoretical and experimental studies of the oil macrlm in lubricatedpoint contact Proc R Soc Lond A 291 520536

Dowson D amp Higginson G R 1966 Elastohydrodynamic lubrication|the fundamentals of roller

and gear lubrication Oxford Pergamon

Drinkwater B W Dwyer-Joyce R S amp Cawley P 1996 A study of the interaction betweenultrasound and a partially contacting solidsolid interface Proc R Soc Lond A 452 26132628

El-Sisi S I amp Shawki G S A 1960 Measurement of oil-macrlm thickness between disks by electricalconductivity Trans ASME J Basic Engng 82 12

Hamilton G M amp Moore S L 1967 A modimacred gauge for investigating an elastohydrodynamiccontact Proc Inst Mech Engrs 182 251

Hamrock B J 1994 Fundamentals of deguid macrlm lubrication McGraw-Hill

Hosten B 1991 Bulk heterogeneous plane-wave propagation through viscoelastic plates andstratimacred media with large values of frequency-domain Ultrasonics 29 445450

Jacobson B O amp Vinet P 1987 A model for the indeguence of pressure on the bulk modulusand the indeguence of temperature on the solidimacrcation pressure for liquid lubricants Trans

ASME J Tribology 109 709

Johnston G J Wayte R amp Spikes H A 1991 The measurement and study of very thinlubricant macrlms in concentrated contacts Tribol Trans 34 187194

Kinra V K Jaminet P T Zhu C amp Iyer V R 1994 Simultaneous measurement of theacoustical properties of a thin-layered medium the inverse problem J Acoust Soc Am 9530593074

Proc R Soc Lond A (2003)

962 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

12

10

08

06

04

02

0 10 20 30 40 50

f (MHz)

refl

ecti

on c

oeff

icie

nt

spring model

continuum model

Figure 3 Comparison between spring-model and continuum-model predictions for theredegection-coeplusmncient spectra from a mineral oil macrlm between two steel elements

3 Acoustic properties of a lubricant macrlm

To determine the thickness of a lubricant shylm using (27) it is necessary to knowboth the density of and the speed of sound through the lubricant The speed ofsound can readily be determined for oil in the bulk from a simple ToF measurementbetween a transducer and a regat reregector For the oil used in these experiments (ShellTurbo T68) the acoustic properties at 20 macrC are shown in table 1

This value is suitable for the analysis of ambient reguid wedges or low-pressurehydrodynamic lubricant shylms However in EHD shylms the lubricant is subjectedto pressures high enough to cause solidishycation and a signishycant change in physi-cal properties The speed of sound through oil under EHD conditions is thereforevery dinoterent to those in the bulk The speed of propagation of a longitudinal wavethrough a medium depends on the density raquo and the bulk modulus B accordingto (see for example Povey 1997)

c =

s

B

raquo (31)

Jacobson amp Vinet (1987) provide a model to determine the inreguence of pressureon the compression and bulk modulus of liquid lubricants They give an equation ofstate to describe the behaviour of the lubricant under pressure p

p =3B0

x2(1 iexcl x)esup2(1iexclx) (32)

and the bulk modulus under pressure is given by

B =B0

x2[2 + (sup2 iexcl 1)x iexcl sup2x2]esup2(1iexclx) (33)

where B0 is the bulk modulus at zero pressure sup2 is a lubricant-specishyc parameterand x is a function of the relative compression

x = 3

r

raquo0

raquop (34)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 963

Table 2 Details of the transducers used in this work

(The focal length and spot size (equation (55)) are determined for a centre-frequency wave inwater)

bandwidth focal length spot sizecentre frequency (iexcl6 dB points) element diameter (in water) (in water)

f (MHz) (MHz) D (mm) F (mm) df (mm)

10 417 127 76 921

25 1732 635 54 522

50 4075 635 25 121

where raquo0 is the density at zero pressure and raquop the density at pressure p These equa-tions are used for the oil both in its liquid state and after it undergoes solidishycationbut employing dinoterent values of sup2 and B0

Jacobson amp Vinet used a high-pressure chamber to measure the compression ofseveral liquid lubricants up to pressures of 22 GPa and determined the parametersfor (32) and (33) For mineral oils the bulk modulus increased from 1517 GPaat atmospheric pressure to 2030 GPa at EHD pressures while the density increasedby 2030 Therefore from (31) the speed of sound within an EHD contact is likelyto be some two to four times greater than that under ambient conditions

Unfortunately there are no test data available specishycally for the lubricant usedin these studies (Shell Turbo T68) However parameters from a similar base oil(extracted from Jacobson amp Vinet (1987)) have been used to determine the relation-ship between bulk modulus density change and pressure Table 1 shows the resultsof this analysis for two oil pressures the lower corresponding to that experienced inthe ball on regat apparatus and the higher to that in ball-bearing contact

4 Ultrasonic redegection measurement apparatus

An ultrasonic pulser-receiver (UPR) generates a high-voltage pulse that causes apiezoelectric transducer to be excited in mechanical resonance The transducer thenemits a broadband pulse of ultrasonic energy As can be seen in shygure 1 this ultra-sonic pulse propagates through the bearing shell is reregected from the lubricant layerand is received by the same transducer Measurements were made using focused ultra-sonic transducers with a range of dinoterent centre frequencies (10 25 and 50 MHz)The transducers were immersed in a water bath and positioned so that the ultrasonicenergy was focused through the water bath and bearing shell onto the lubricant layerTable 2 details the bandwidth geometry and focusing properties of the transducersused

The pulse reregected from the lubricant layer was amplishyed and stored on a dig-ital oscilloscope The stored reregected signals were passed to a PC for processingFigure 4 shows a schematic of the apparatus and data signals Software (written inthe LabView environment) was written to control the UPR receive reregection signalsfrom the oscilloscope perform the required signal processing and display the requiredresults

Proc R Soc Lond A (2003)

964 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

ball bearing

raceway

focusedultrasonictransducer

lubricant film

controlsignal

digital scope

downloadwaveform to PC

UPR

PC

Figure 4 Schematic of ultrasonic pulsing and receiving system

transducer

water tank

shim

glasssheets

positioning scale

Figure 5 Schematic of the apparatus used for generatingthin liquid macrlms between two degat surfaces

5 Measurement of a stationary liquid layer

Initial experiments were performed on thin liquid layers between stationary solidsurfaces Two conshygurations were chosen a water wedge between optical glass regatsand an oil shylm between two eccentric cylinders The former apparatus was used toproduce a wide range of measurable liquid-layer thickness The latter was designed toinvestigate the enotects of the curvature of the solid surfaces and the use of a mineraloil as the liquid medium

(a) Liquid-wedge apparatus

Shims of various thickness were used to separate sheets of regoat glass which werethen immersed in a water tank as shown in shygure 5 The ultrasonic transducerswere also immersed in the water tank and mounted above the liquid wedge on acomputer-controlled xy positioning frame The ultrasonic pulsing and receiving wascontrolled by the apparatus as shown in shygure 4

The shyrst step in the procedure was to determine the frequency characteristics of theincident ultrasonic pulse The bottom glass plate was removed and the pulse reregected

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 965

6 7 8 9 10 11

10

09

08

07

06

05

04

03

02

refl

ect

ion c

oef

fici

ent

18 mm

53 mm

89 mm

124 mm

159 mm

195 mm

(a)

10

08

06

04

02

0

refl

ect

ion c

oeff

icie

nt

15 17 19 21 23 25 27 29 31 33

f (MHz)

125 mm 375 mm 50 mm 625 mm 75 mm(b)

Figure 6 Measured redegection-coeplusmncient spectra for a range of deguid macrlm thicknesses using(a) a 10 MHz and (b) a 25 MHz centre-frequency transducer

from the glasswater interface recorded This time-domain signal was converted tothe frequency domain via a fast Fourier transform and stored as a reference Aref Inthis way

Aref(f) = I(f)Rgw (51)

where I(f ) is the frequency-response characteristic of the incident pulse and Rgw

is the glasswater reregection coemacrcient given by (21) The bottom plate was thenrepositioned and measurements of the pulse reregected from the reguid shylm were recordedat various locations along the reguid wedge This measurement signal Am eas can bewritten as

Am eas (f) = I(f)Rl(f) (52)

Proc R Soc Lond A (2003)

966 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

25

20

15

10

5

0

film

thic

knes

s (m

m)

60 65 70 75 80 85 90 95 100 105 110

f (MHz)

Figure 7 Film-thickness results determined by the application ofthe spring model to the redegection spectra of macrgure 6a

where Rl(f) is the reregection-coemacrcient spectrum of the lubricant layer which canthen be obtained by combining (51) and (52)

Rl(f) =Am eas (f)

Aref(f)Rgw (53)

Figure 6 shows two sets of reregection-coemacrcient spectra of liquid layers in a liquid-wedge experiment recorded using two dinoterent wide-band transducers for a rangeof shylm thickness The thickness of the liquid layer at any measuring location wasestimated from the geometry of the reguid wedge formed by the shim

From shygure 6b it can be seen that at higher shylm thicknesses resonant frequencies(observed as minima in the reregection-coemacrcient spectra) are visible When these res-onances occur the layer thickness can be readily determined from (23) For thinnerliquid layers andor when using lower-frequency transducers the resonance is notobserved as it occurs beyond the frequency range of the transducer However theshape of the reregection-coemacrcient spectrum below resonance can be used to predictthe thickness of the liquid layer though the application of the spring model (equa-tion (27))

The stinotness of the layer can be measured over a range of frequencies with onetransducer As the stinotness at a single frequency is sumacrcient to enable prediction ofthe reguid-layer thickness there is some redundancy in the data that can be used as amethod of checking the accuracy of the spring model Figure 7 shows the data given inshygure 6a converted to shylm thickness via (27) over the bandwidth of the transducerFrom shygure 7 it can be seen that for the lower shylm-thickness values the curvesare horizontal This indicates a good measurement as the shylm thickness cannot bea function of the frequency with which it is measured However for the top curvethe model does not correctly convert the reregection coemacrcient to a constant layerthickness This is because as the reregection coemacrcient tends to unity so the springmodel (equation (27)) becomes prone to numerical error For the next curve down

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 967

0

10

20

30

40

50

70

mea

sure

d f

ilm

thic

kness

(m

m)

60

predicted film thickness (mm)

10 20 30 40 50 60 70

Figure 8 Film-thickness values measured by ultrasonic redegection compared withpredictions of the thickness determined from the geometry of the deguid wedge

at the higher frequencies the same happens This represents a limit of the spring-model approach and to measure these thicker shylms either lower frequencies shouldbe used so R is lower or higher frequencies used and the location of resonancesdetermined

Figure 8 shows ultrasonic measurements of the thickness of the liquid shylm com-pared with the geometrical prediction of the layer thickness The data below 25 mmcorrespond to measurements performed using the spring model while the data above25 mm have been determined from the measurement of shylm resonances Agreementis good (and a straight line is observed) but in practice the measured liquid-layerthickness tends to be slightly larger than that of the shim This is likely to becaused by either some thin residual of water between the shim of the glass plateor by deformation of the shim where it has been cut Each of these enotects wouldtend to make the liquid layer thicker and hence explain the dinoterence seen in shyg-ure 8

(b) Annular oil-macrlm apparatus

Figure 9 shows the apparatus to create an oil wedge between a ring and a shaft Thering and shaft were made from aluminium The ringshaft interface had a nominaldiameter of 70 mm and a diametral clearance of 100 mm The shaft was spring loadedagainst the ring By changing the position of the loading point the gap thicknessin the region above the transducer could be varied The gap was shylled with mineraloil (Shell Turbo T68) through a small shyller hole A 25 MHz focused transducer waslocated in a water bath beneath the assembly The transducer was positioned so thatthe wave was focused on the reguid layer

Figure 10 shows a plot of the shylm thickness determined from the reregection mea-surements for various angular positions of the loading point relative to the ultra-sonic measurement position In this case all the shylms were measured using theshylm-resonance method The theoretical width of annular gap h between eccentriccylinders is obtained from geometry

h = R1

middot

1 iexcl

micro

R1 iexcl R2

R1

para2

sin2 iquest

cedil1=2

iexcl R2 + (R1 iexcl R2) cos iquest (54)

Proc R Soc Lond A (2003)

968 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

transducer

water tank

measurement zone

oil-filled annulus

tension spring

aluminium cylinders

Figure 9 Apparatus used to create an annular oil macrlm for ultrasonic-redegection experiments

film

thic

knes

s (m

m)

100

90

80

70

60

50

40

30

20

10

0

angular position (deg)

-180 -135 -90 -45 0 45 90 135 180

ultrasonic measurements

mathematical solution

Figure 10 Film-thickness values measured by ultrasonic redegection for an annular macrlm betweentwo eccentric cylinders Experimental results are compared with the geometrical solution

where R1 and R2 are the radii of the bush and shaft respectively and rsquo is theangle measured from the point of contact Equation (54) is included in shygure 10 forcomparison and a good correlation was observed

To reduce the enotects of the curvature of the lubricated interface the transducersused in this experiment focus the wave onto the oil layer The spot size of the focusedwave varies with frequency according to the relationship (Silk 1984)

df(iexcl6 d B) =1028F c

fD (55)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 969

steel disc water bath

oil meniscus

rotating steel ball

transducer

hydraulic load

motor drive

Figure 11 Schematic of the experimental apparatus used to generatean EHD macrlm for a ball sliding on a degat

where df is the diameter of the spot size (where the signal has reduced to iexcl6 dBof its peak value) F is the transducer focusing length f is the wave frequencyc is the speed of sound in water and D is the diameter of the piezoelectric elementFor a 25 MHz frequency wave this corresponds to a spot size in water of 522 mmThis is small compared with the radius of the shaftbush apparatus So essentiallythe transducer is receiving signals back from a regat region of constant shylm thick-ness and the curvature has little enotect The good agreement between experimen-tal and theoretical liquid-layer thickness shown in shygure 10 further validates thishypothesis

6 Measurement of dynamic lubricating macrlms

An EHD lubricant shylm forms between rolling or sliding non-conformal contactsTypically the thickness of the oil layer is in the region of 011 mm This is withinthe range of the possible measurement by ultrasonic means and within the spring-model regime of ultrasonic response In this work EHD shylms have been measuredin a model rig containing a single stationary lubricated contact and in a rolling-element bearing where the lubricant shylm is transient (with respect to the trans-ducer)

(a) Ball on disc EHD lubrication apparatus

Figure 11 shows the apparatus used to generate a single EHD lubricated contactA steel ball is supported on rollers and hydraulically loaded onto the underside ofa steel disc The ball is rotated at constant speed by an electric motor througha gear box and quill shaft The steel disc is held stationary such that the ball iscompletely sliding against the underside of the disc This apparatus is a modishyed`optical elastohydrodynamicrsquo apparatus (originally developed by Cameron amp Gohar(1966)) where the semi-reregective rotating glass disc has been replaced by a station-

Proc R Soc Lond A (2003)

970 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

005

010

015

020

025

030

035

040

0 02 04 06 08 10 12 14

lubri

can

t fi

lm thic

kness

(m

m)

entrainment speed (m s-1)

theoretical solution a = 015 mmmeasurements a = 015 mmtheoretical solution a = 01 mmmeasurements a = 01 mm

Figure 12 EHD lubricant-macrlm-thickness variation with ball-sliding speed for two loadsUltrasonic-redegection measurements are compared with a theoretical solution

ary steel disc and the microscope replaced by an ultrasonic transducer The balldisc contact was regooded with a mineral oil (Shell Turbo T68) which is entrainedinto the contact to form an EHD shylm A 50 MHz focused transducer was mountedabove the contact in a water bath The transducer was positioned directly abovethe contact region and at a distance such that the wave is focused on the balldiscinterface

Reregected pulses were recorded from the discball interface as the ball rotationalspeed and load were varied A reference spectrum was obtained by recording the pulsereregected when the ball was out of contact with the disc but the disc was still regoodedwith oil As in the wedge experiment the reference and lubricant-layer measurementswere used in (32) to obtain the reregection-coemacrcient spectrum of the lubricant layerA series of reregection coemacrcient spectra were then recorded from the discball contactas the sliding speed was increased The spring model (equation (27)) was used todetermine the shylm thickness from these spectra An automated LabView interfacewas written to record the spectra divide by a reference and convert the data intoshylm thickness (as shown in shygure 6) As discussed in x 3 above the density and speedof sound of the oil used in (27) are those at contact pressure (in this case 08 GPa)and not those in the bulk

Figure 12 shows the measured variation in shylm thickness determined from thereregection coemacrcient spectra as the speed is increased for two load cases (giving con-tact radii a of 01 and 015 mm) For this lubrication case a theoretical predictionof the oil-shylm thickness can be obtained from the regression equations of Dowson ampHigginson (1966) The central shylm thickness hc is expressed as a regression equationconsisting of shyve non-dimensional parameters

Hc = 269U 067G053W iexcl0067(1 iexcl 061eiexcl073k) (61)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 971

test rolling bearing

measurement zone

hydraulic loading

focusing transducer

water bath

belt and pulley drive

Figure 13 Schematic of apparatus used for ultrasonic measurementsof macrlm thickness in rolling-element bearings

where

Hc =hc

Rx

W =P

2EcurrenR2x

U =sup20u

2EcurrenRx

k = 103

micro

Ry

Rx

para064

G = 2notEcurren

where Ecurren is the reduced modulus Rx and Ry are the reduced radii in the paralleland transverse directions u is the mean surface speed P is the applied contact loadsup20 is the viscosity of oil in the inlet and not is its pressure-viscosity coemacrcient

The predictions of (61) for the two load cases are plotted in shygure 12 The agree-ment between the theoretical solution and the experimental data is good Typicallythe measured data are repeatable to within sect20 The oil shylm generated by theapparatus is not completely stable To directly observe the lubricant shylm the steeldisc was replaced by the glass disc and the shylm monitored visually A certain amountof shylm reguctuation was observed during normal running (caused by a slight processingof the ball on its supporting rollers) Notwithstanding the results are encouragingbecause this indicates that both the integrity of the ultrasonic method and alsothat the speed of sound of the lubricating oil compares well with predictions fromhigh-pressure measurements

(b) Rolling bearing lubricant-macrlm measurement

The duration of the ultrasonic pulses used in this work was short Spatially thepulse width was typically three wavelengths in length A 25 MHz wave travelling insteel results in a pulse duration of 01 ms Therefore it is feasible to record the shylmthickness in a rolling element moving past the focal point of an ultrasonic transducer

The approach has been used to measure shylm thickness in a 6410 deep-grooveball bearing Figure 13 shows a schematic of the bearing and the positioning of thetransducer The 25 MHz transducer (see table 2 for details) was located in a small

Proc R Soc Lond A (2003)

972 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

0

01

02

03

04

05

07

01 02 03 04 05 06 07

theo

reti

cal

film

thic

knes

s pre

dic

tion (

mm

)

45 kN 112 RPM 60 kN 72 RPM

60 kN 103 RPM 60 kN 128 RPM

60 kN 135 RPM 60 kN 137 RPM

60 kN 178 RPM 60 kN 195 RPM

60 kN 297 RPM 60 kN 375 RPM

75 kN 48 RPM 75 kN 124 RPM

06

measured film thickness (mm)

Figure 14 Comparison of rolling-element-bearing macrlm thickness measured byan ultrasonic means with EHD theoretical solution

water bath machined out of the bearing bush The transducer was spherically focusedand positioned in the water bath so that the wave was focused on the contact betweena ball and the raceway The bearing was loaded hydraulically and rotated by anelectric motor The bearing cavity was regooded with a mineral oil (Shell Turbo T68) Athermocouple was positioned on the outer raceway near the ultrasonic measurementpoint The bearing was loaded to give a contact eclipse between the ball and theouter raceway of semi-major and semi-minor axes 115 and 08 mm respectivelyThe bearing was then rotated and the transducer set to continuously pulse at arepetition rate of 10 kHz

The focal spot size of the transducer was ca 500 mm The maximum rotationalspeed of the bearing in these tests was 375 rpm At this rotational speed theregion of focused ultrasound would remain completely within the lubricated con-tact for ca 05 ms This allowed approximately shyve discrete pulses of ultrasound tobe reregected from the lubricant shylm as each ball passed through the measurementzone Initially a reference reregected pulse was recorded when the bearing was station-ary and there was no ball located over the measurement zone (although the cavitywas still shylled with oil) If a pulse is incident on an EHD shylm its amplitude is reducedbecause part of the wave has been transmitted through the oil shylm into the ball Bycontinuously monitoring the signals reregected from the raceway measurements of theball-raceway contacts were made Of the shyve pulses reregected from the ball-racewaycontact the lowest amplitude pulse was selected for analysis This pulse correspondsto the thinnest measured shylm thickness It should be noted that the resolution of thefocused transducer and the measurement interval are such that it was not possibleto record the horseshoe-shaped minimum shylm-thickness constriction at the contactexit The selected pulse was analysed shyrstly using (53) to calculate the reregection

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 973

film

thic

knes

s (m

m)

1000

100

10

1

01

001

00010 10 20 30 40 50 60

f (MHz)

time of flight limit

resonance method limit

spring model upper limit (R = 09)

spring model lower limit (R = 01)

Figure 15 Limits of operation for macrlm-thickness measurement by ultrasonic means

coemacrcient and then using the spring model to predict the shylm thickness The speedof sound in the oil in the contact is set to c = 4400 m siexcl1 (determined using themethod described in x 3)

Figure 14 shows the measured shylm thickness plotted against a prediction of theshylm thickness from the solution for an elliptical contact of Dowson amp Higginson(1966) (equation (61)) The bearing and lubricant heats up during operation Thetemperature of the entrained oil was monitored and used to determine an appropriateviscosity with which to calculate the shylm thickness in (61) This was why the resultswere not plotted as shylm thickness against speed (as in shygure 11) because viscositywas varying throughout the test

The results in shygure 14 show good agreement between measured lubricant-shylmthickness and that predicted by the EHD regression equations The spread along thex-axis shows the variation in shylm for nominally the same bearing operating conditions(load speed and oil temperature) At this stage it is not clear whether this scatteris a result of the measurement process or whether this is the actual shylm thicknessin the bearing It is worth noting that this measurement process could be improvedif the exact position of the ball could be related to the ultrasonic measurement soallowing a more precise measurement of the minimum shylm thickness

7 Discussion limits of operation

It is instructive to consider the limits of shylm-thickness measurement for a given ultra-sonic frequency The simplest method for determining the thickness of a lubricantlayer providing it is sumacrciently thick is by measuring the ToF through the layerA reregection occurs at the layer front face and another at the back face The thick-ness is readily obtained from the time between the arrival of these pulses multipliedby the acoustic velocity For the method to work the two reregected pulses must besumacrciently discrete and so the propagation distance must be greater than the pulse

Proc R Soc Lond A (2003)

974 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

width and so the minimum shylm thickness detectable by this method is given by

h gtnc

2f (71)

where n is the number of wavelengths in the ultrasonic pulse typically around threeThis measurement limit is plotted in shygure 15 as the minimum frequency requiredto measure a given shylm thickness Conventional ultrasonic non-destructive testingis generally restricted by losses in the propagating media (steel in this case) tofrequencies below 4060 MHz From (71) this means that the ToF method is onlypractically useful for layers of thickness greater than 40 mm This is thicker than thatfound on most commercial bearing systems

A lubricant layer resonates at a frequency given by (23) This equation also givesthe low thickness limit for this technique as the upper frequency output by a giventransducer determined the lowest measurable layer thickness This limit is also shownin shygure 15 for the shyrst through-thickness mode (ie m = 1) So using the highestpractical frequencies shylms greater than 10 mm are measurable by the shylm-resonancemethod

The upper limit of shylm thickness measurable using the spring-model approach isreached as R tends to unity in (27) Experience shows that measurements of R lessthan 09 yield satisfactory results The lowest shylm thickness measurable will dependon the smallest possible value of R This in turn will depend on the signal-to-noiseratio A signal-to-noise ratio of 60 dB is typical for conventional ultrasonic non-destructive testing systems The noise amplitude is thus 1

1000of the pulse amplitude

In the case of a measurement on a real bearing the achievable signal-to-noise ratiowill be reduced by the transducer-bearing reregection coemacrcient and by the attenuationin the bearing shell This means that the pulse incident in the reguid shylm will bereduced from that output by the transducer by a factor of shyve (as a conservativeestimate) Further it is assumed that for reliable measurements a pulse reregectedfrom the oil layer should have an amplitude approximately 20 times that of the noiselevel This results in a minimum measurable reregection coemacrcient of R = 01 Therelationships between the shylm thickness and the transducer frequency for the upperlimit when R = 09 and the lower where R = 01 are shown in shygure 15

This indicates that for a measuring frequency of 60 MHz a lubricant shylm of 2 nmis measurable This opens up the possibility of measuring boundary-type lubricantshylms between machine elements However the models presented here are designedfor a parallel-sided oil layer completely separating the smooth bearing surface If atthese low shylm thickness metal-to-metal contact occurs then transmission will occurat this location In this case some alternative method for interpreting reregectioncoemacrcients will be needed

8 Conclusions

Ultrasound is reregected from the lubricant shylm between bearing surfaces It is possibleto deduce the thickness of the lubricant shylm by comparing the frequency spectrumof the reregected pulse with that of the incident pulse The response of the lubricantlayer to an ultrasonic pulse has been modelled using both a spring-model methodand a continuum method The spring model is suitable for thin lubricant shylms inwhich the wavelength of the ultrasound is much larger than the layer thickness The

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 975

continuum model is valid for all layer thicknesses and allows the prediction of thethrough-thickness resonant frequencies of the lubricant layers Measurement of thesethrough-thickness resonances also provides a means of measuring the layer thickness

Experiments on reguid layers between regat plates and eccentric rings have demon-strated that ultrasound can suitably measure a wide range of liquid layer thicknessThe EHD lubricant shylm that forms between a ball sliding on a regat surface hasalso been measured ultrasonically The measured results agree well with theoreti-cal predictions taking into account the greatly increased speed of sound throughthe lubricant when it is under high pressure Films in the range 50500 nm wererecorded

The approach can also be used to measure shylm thickness in a rolling-elementbearing An ultrasonic transducer was mounted on the bearing raceway and thepulse reregected from the lubricant layer generated as the ball passes was recordedAgain measured results agreed well with theoretical predictions

The lower limit of measurement by this method depends on the signal-to-noiseratio A continuum model showed that using frequencies up to 60 MHz permits themeasurement of 2 nm thick shylms There is no upper limit to shylm-thickness measure-ment Thick shylms (greater than 40 mm) can be measured by a time-of-regight methodFilms of intermediate thickness can be determined by measuring the frequency atwhich the shylm resonates

This work was funded by a grant from the UK Engineering and Physical Sciences ResearchCouncil under the ROPA programme The authors acknowledge the help of Phil Harper of theUniversity of Sheplusmneld for his assistance with some of the measurements

References

Astridge D G amp Longmacreld M D 1967 Capacitance measurement and oil macrlm thickness in alarge radius disc and ring machine Proc Inst Mech Engrs 182 8996

Cameron A amp Gohar R 1966 Theoretical and experimental studies of the oil macrlm in lubricatedpoint contact Proc R Soc Lond A 291 520536

Dowson D amp Higginson G R 1966 Elastohydrodynamic lubrication|the fundamentals of roller

and gear lubrication Oxford Pergamon

Drinkwater B W Dwyer-Joyce R S amp Cawley P 1996 A study of the interaction betweenultrasound and a partially contacting solidsolid interface Proc R Soc Lond A 452 26132628

El-Sisi S I amp Shawki G S A 1960 Measurement of oil-macrlm thickness between disks by electricalconductivity Trans ASME J Basic Engng 82 12

Hamilton G M amp Moore S L 1967 A modimacred gauge for investigating an elastohydrodynamiccontact Proc Inst Mech Engrs 182 251

Hamrock B J 1994 Fundamentals of deguid macrlm lubrication McGraw-Hill

Hosten B 1991 Bulk heterogeneous plane-wave propagation through viscoelastic plates andstratimacred media with large values of frequency-domain Ultrasonics 29 445450

Jacobson B O amp Vinet P 1987 A model for the indeguence of pressure on the bulk modulusand the indeguence of temperature on the solidimacrcation pressure for liquid lubricants Trans

ASME J Tribology 109 709

Johnston G J Wayte R amp Spikes H A 1991 The measurement and study of very thinlubricant macrlms in concentrated contacts Tribol Trans 34 187194

Kinra V K Jaminet P T Zhu C amp Iyer V R 1994 Simultaneous measurement of theacoustical properties of a thin-layered medium the inverse problem J Acoust Soc Am 9530593074

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 963

Table 2 Details of the transducers used in this work

(The focal length and spot size (equation (55)) are determined for a centre-frequency wave inwater)

bandwidth focal length spot sizecentre frequency (iexcl6 dB points) element diameter (in water) (in water)

f (MHz) (MHz) D (mm) F (mm) df (mm)

10 417 127 76 921

25 1732 635 54 522

50 4075 635 25 121

where raquo0 is the density at zero pressure and raquop the density at pressure p These equa-tions are used for the oil both in its liquid state and after it undergoes solidishycationbut employing dinoterent values of sup2 and B0

Jacobson amp Vinet used a high-pressure chamber to measure the compression ofseveral liquid lubricants up to pressures of 22 GPa and determined the parametersfor (32) and (33) For mineral oils the bulk modulus increased from 1517 GPaat atmospheric pressure to 2030 GPa at EHD pressures while the density increasedby 2030 Therefore from (31) the speed of sound within an EHD contact is likelyto be some two to four times greater than that under ambient conditions

Unfortunately there are no test data available specishycally for the lubricant usedin these studies (Shell Turbo T68) However parameters from a similar base oil(extracted from Jacobson amp Vinet (1987)) have been used to determine the relation-ship between bulk modulus density change and pressure Table 1 shows the resultsof this analysis for two oil pressures the lower corresponding to that experienced inthe ball on regat apparatus and the higher to that in ball-bearing contact

4 Ultrasonic redegection measurement apparatus

An ultrasonic pulser-receiver (UPR) generates a high-voltage pulse that causes apiezoelectric transducer to be excited in mechanical resonance The transducer thenemits a broadband pulse of ultrasonic energy As can be seen in shygure 1 this ultra-sonic pulse propagates through the bearing shell is reregected from the lubricant layerand is received by the same transducer Measurements were made using focused ultra-sonic transducers with a range of dinoterent centre frequencies (10 25 and 50 MHz)The transducers were immersed in a water bath and positioned so that the ultrasonicenergy was focused through the water bath and bearing shell onto the lubricant layerTable 2 details the bandwidth geometry and focusing properties of the transducersused

The pulse reregected from the lubricant layer was amplishyed and stored on a dig-ital oscilloscope The stored reregected signals were passed to a PC for processingFigure 4 shows a schematic of the apparatus and data signals Software (written inthe LabView environment) was written to control the UPR receive reregection signalsfrom the oscilloscope perform the required signal processing and display the requiredresults

Proc R Soc Lond A (2003)

964 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

ball bearing

raceway

focusedultrasonictransducer

lubricant film

controlsignal

digital scope

downloadwaveform to PC

UPR

PC

Figure 4 Schematic of ultrasonic pulsing and receiving system

transducer

water tank

shim

glasssheets

positioning scale

Figure 5 Schematic of the apparatus used for generatingthin liquid macrlms between two degat surfaces

5 Measurement of a stationary liquid layer

Initial experiments were performed on thin liquid layers between stationary solidsurfaces Two conshygurations were chosen a water wedge between optical glass regatsand an oil shylm between two eccentric cylinders The former apparatus was used toproduce a wide range of measurable liquid-layer thickness The latter was designed toinvestigate the enotects of the curvature of the solid surfaces and the use of a mineraloil as the liquid medium

(a) Liquid-wedge apparatus

Shims of various thickness were used to separate sheets of regoat glass which werethen immersed in a water tank as shown in shygure 5 The ultrasonic transducerswere also immersed in the water tank and mounted above the liquid wedge on acomputer-controlled xy positioning frame The ultrasonic pulsing and receiving wascontrolled by the apparatus as shown in shygure 4

The shyrst step in the procedure was to determine the frequency characteristics of theincident ultrasonic pulse The bottom glass plate was removed and the pulse reregected

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 965

6 7 8 9 10 11

10

09

08

07

06

05

04

03

02

refl

ect

ion c

oef

fici

ent

18 mm

53 mm

89 mm

124 mm

159 mm

195 mm

(a)

10

08

06

04

02

0

refl

ect

ion c

oeff

icie

nt

15 17 19 21 23 25 27 29 31 33

f (MHz)

125 mm 375 mm 50 mm 625 mm 75 mm(b)

Figure 6 Measured redegection-coeplusmncient spectra for a range of deguid macrlm thicknesses using(a) a 10 MHz and (b) a 25 MHz centre-frequency transducer

from the glasswater interface recorded This time-domain signal was converted tothe frequency domain via a fast Fourier transform and stored as a reference Aref Inthis way

Aref(f) = I(f)Rgw (51)

where I(f ) is the frequency-response characteristic of the incident pulse and Rgw

is the glasswater reregection coemacrcient given by (21) The bottom plate was thenrepositioned and measurements of the pulse reregected from the reguid shylm were recordedat various locations along the reguid wedge This measurement signal Am eas can bewritten as

Am eas (f) = I(f)Rl(f) (52)

Proc R Soc Lond A (2003)

966 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

25

20

15

10

5

0

film

thic

knes

s (m

m)

60 65 70 75 80 85 90 95 100 105 110

f (MHz)

Figure 7 Film-thickness results determined by the application ofthe spring model to the redegection spectra of macrgure 6a

where Rl(f) is the reregection-coemacrcient spectrum of the lubricant layer which canthen be obtained by combining (51) and (52)

Rl(f) =Am eas (f)

Aref(f)Rgw (53)

Figure 6 shows two sets of reregection-coemacrcient spectra of liquid layers in a liquid-wedge experiment recorded using two dinoterent wide-band transducers for a rangeof shylm thickness The thickness of the liquid layer at any measuring location wasestimated from the geometry of the reguid wedge formed by the shim

From shygure 6b it can be seen that at higher shylm thicknesses resonant frequencies(observed as minima in the reregection-coemacrcient spectra) are visible When these res-onances occur the layer thickness can be readily determined from (23) For thinnerliquid layers andor when using lower-frequency transducers the resonance is notobserved as it occurs beyond the frequency range of the transducer However theshape of the reregection-coemacrcient spectrum below resonance can be used to predictthe thickness of the liquid layer though the application of the spring model (equa-tion (27))

The stinotness of the layer can be measured over a range of frequencies with onetransducer As the stinotness at a single frequency is sumacrcient to enable prediction ofthe reguid-layer thickness there is some redundancy in the data that can be used as amethod of checking the accuracy of the spring model Figure 7 shows the data given inshygure 6a converted to shylm thickness via (27) over the bandwidth of the transducerFrom shygure 7 it can be seen that for the lower shylm-thickness values the curvesare horizontal This indicates a good measurement as the shylm thickness cannot bea function of the frequency with which it is measured However for the top curvethe model does not correctly convert the reregection coemacrcient to a constant layerthickness This is because as the reregection coemacrcient tends to unity so the springmodel (equation (27)) becomes prone to numerical error For the next curve down

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 967

0

10

20

30

40

50

70

mea

sure

d f

ilm

thic

kness

(m

m)

60

predicted film thickness (mm)

10 20 30 40 50 60 70

Figure 8 Film-thickness values measured by ultrasonic redegection compared withpredictions of the thickness determined from the geometry of the deguid wedge

at the higher frequencies the same happens This represents a limit of the spring-model approach and to measure these thicker shylms either lower frequencies shouldbe used so R is lower or higher frequencies used and the location of resonancesdetermined

Figure 8 shows ultrasonic measurements of the thickness of the liquid shylm com-pared with the geometrical prediction of the layer thickness The data below 25 mmcorrespond to measurements performed using the spring model while the data above25 mm have been determined from the measurement of shylm resonances Agreementis good (and a straight line is observed) but in practice the measured liquid-layerthickness tends to be slightly larger than that of the shim This is likely to becaused by either some thin residual of water between the shim of the glass plateor by deformation of the shim where it has been cut Each of these enotects wouldtend to make the liquid layer thicker and hence explain the dinoterence seen in shyg-ure 8

(b) Annular oil-macrlm apparatus

Figure 9 shows the apparatus to create an oil wedge between a ring and a shaft Thering and shaft were made from aluminium The ringshaft interface had a nominaldiameter of 70 mm and a diametral clearance of 100 mm The shaft was spring loadedagainst the ring By changing the position of the loading point the gap thicknessin the region above the transducer could be varied The gap was shylled with mineraloil (Shell Turbo T68) through a small shyller hole A 25 MHz focused transducer waslocated in a water bath beneath the assembly The transducer was positioned so thatthe wave was focused on the reguid layer

Figure 10 shows a plot of the shylm thickness determined from the reregection mea-surements for various angular positions of the loading point relative to the ultra-sonic measurement position In this case all the shylms were measured using theshylm-resonance method The theoretical width of annular gap h between eccentriccylinders is obtained from geometry

h = R1

middot

1 iexcl

micro

R1 iexcl R2

R1

para2

sin2 iquest

cedil1=2

iexcl R2 + (R1 iexcl R2) cos iquest (54)

Proc R Soc Lond A (2003)

968 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

transducer

water tank

measurement zone

oil-filled annulus

tension spring

aluminium cylinders

Figure 9 Apparatus used to create an annular oil macrlm for ultrasonic-redegection experiments

film

thic

knes

s (m

m)

100

90

80

70

60

50

40

30

20

10

0

angular position (deg)

-180 -135 -90 -45 0 45 90 135 180

ultrasonic measurements

mathematical solution

Figure 10 Film-thickness values measured by ultrasonic redegection for an annular macrlm betweentwo eccentric cylinders Experimental results are compared with the geometrical solution

where R1 and R2 are the radii of the bush and shaft respectively and rsquo is theangle measured from the point of contact Equation (54) is included in shygure 10 forcomparison and a good correlation was observed

To reduce the enotects of the curvature of the lubricated interface the transducersused in this experiment focus the wave onto the oil layer The spot size of the focusedwave varies with frequency according to the relationship (Silk 1984)

df(iexcl6 d B) =1028F c

fD (55)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 969

steel disc water bath

oil meniscus

rotating steel ball

transducer

hydraulic load

motor drive

Figure 11 Schematic of the experimental apparatus used to generatean EHD macrlm for a ball sliding on a degat

where df is the diameter of the spot size (where the signal has reduced to iexcl6 dBof its peak value) F is the transducer focusing length f is the wave frequencyc is the speed of sound in water and D is the diameter of the piezoelectric elementFor a 25 MHz frequency wave this corresponds to a spot size in water of 522 mmThis is small compared with the radius of the shaftbush apparatus So essentiallythe transducer is receiving signals back from a regat region of constant shylm thick-ness and the curvature has little enotect The good agreement between experimen-tal and theoretical liquid-layer thickness shown in shygure 10 further validates thishypothesis

6 Measurement of dynamic lubricating macrlms

An EHD lubricant shylm forms between rolling or sliding non-conformal contactsTypically the thickness of the oil layer is in the region of 011 mm This is withinthe range of the possible measurement by ultrasonic means and within the spring-model regime of ultrasonic response In this work EHD shylms have been measuredin a model rig containing a single stationary lubricated contact and in a rolling-element bearing where the lubricant shylm is transient (with respect to the trans-ducer)

(a) Ball on disc EHD lubrication apparatus

Figure 11 shows the apparatus used to generate a single EHD lubricated contactA steel ball is supported on rollers and hydraulically loaded onto the underside ofa steel disc The ball is rotated at constant speed by an electric motor througha gear box and quill shaft The steel disc is held stationary such that the ball iscompletely sliding against the underside of the disc This apparatus is a modishyed`optical elastohydrodynamicrsquo apparatus (originally developed by Cameron amp Gohar(1966)) where the semi-reregective rotating glass disc has been replaced by a station-

Proc R Soc Lond A (2003)

970 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

005

010

015

020

025

030

035

040

0 02 04 06 08 10 12 14

lubri

can

t fi

lm thic

kness

(m

m)

entrainment speed (m s-1)

theoretical solution a = 015 mmmeasurements a = 015 mmtheoretical solution a = 01 mmmeasurements a = 01 mm

Figure 12 EHD lubricant-macrlm-thickness variation with ball-sliding speed for two loadsUltrasonic-redegection measurements are compared with a theoretical solution

ary steel disc and the microscope replaced by an ultrasonic transducer The balldisc contact was regooded with a mineral oil (Shell Turbo T68) which is entrainedinto the contact to form an EHD shylm A 50 MHz focused transducer was mountedabove the contact in a water bath The transducer was positioned directly abovethe contact region and at a distance such that the wave is focused on the balldiscinterface

Reregected pulses were recorded from the discball interface as the ball rotationalspeed and load were varied A reference spectrum was obtained by recording the pulsereregected when the ball was out of contact with the disc but the disc was still regoodedwith oil As in the wedge experiment the reference and lubricant-layer measurementswere used in (32) to obtain the reregection-coemacrcient spectrum of the lubricant layerA series of reregection coemacrcient spectra were then recorded from the discball contactas the sliding speed was increased The spring model (equation (27)) was used todetermine the shylm thickness from these spectra An automated LabView interfacewas written to record the spectra divide by a reference and convert the data intoshylm thickness (as shown in shygure 6) As discussed in x 3 above the density and speedof sound of the oil used in (27) are those at contact pressure (in this case 08 GPa)and not those in the bulk

Figure 12 shows the measured variation in shylm thickness determined from thereregection coemacrcient spectra as the speed is increased for two load cases (giving con-tact radii a of 01 and 015 mm) For this lubrication case a theoretical predictionof the oil-shylm thickness can be obtained from the regression equations of Dowson ampHigginson (1966) The central shylm thickness hc is expressed as a regression equationconsisting of shyve non-dimensional parameters

Hc = 269U 067G053W iexcl0067(1 iexcl 061eiexcl073k) (61)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 971

test rolling bearing

measurement zone

hydraulic loading

focusing transducer

water bath

belt and pulley drive

Figure 13 Schematic of apparatus used for ultrasonic measurementsof macrlm thickness in rolling-element bearings

where

Hc =hc

Rx

W =P

2EcurrenR2x

U =sup20u

2EcurrenRx

k = 103

micro

Ry

Rx

para064

G = 2notEcurren

where Ecurren is the reduced modulus Rx and Ry are the reduced radii in the paralleland transverse directions u is the mean surface speed P is the applied contact loadsup20 is the viscosity of oil in the inlet and not is its pressure-viscosity coemacrcient

The predictions of (61) for the two load cases are plotted in shygure 12 The agree-ment between the theoretical solution and the experimental data is good Typicallythe measured data are repeatable to within sect20 The oil shylm generated by theapparatus is not completely stable To directly observe the lubricant shylm the steeldisc was replaced by the glass disc and the shylm monitored visually A certain amountof shylm reguctuation was observed during normal running (caused by a slight processingof the ball on its supporting rollers) Notwithstanding the results are encouragingbecause this indicates that both the integrity of the ultrasonic method and alsothat the speed of sound of the lubricating oil compares well with predictions fromhigh-pressure measurements

(b) Rolling bearing lubricant-macrlm measurement

The duration of the ultrasonic pulses used in this work was short Spatially thepulse width was typically three wavelengths in length A 25 MHz wave travelling insteel results in a pulse duration of 01 ms Therefore it is feasible to record the shylmthickness in a rolling element moving past the focal point of an ultrasonic transducer

The approach has been used to measure shylm thickness in a 6410 deep-grooveball bearing Figure 13 shows a schematic of the bearing and the positioning of thetransducer The 25 MHz transducer (see table 2 for details) was located in a small

Proc R Soc Lond A (2003)

972 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

0

01

02

03

04

05

07

01 02 03 04 05 06 07

theo

reti

cal

film

thic

knes

s pre

dic

tion (

mm

)

45 kN 112 RPM 60 kN 72 RPM

60 kN 103 RPM 60 kN 128 RPM

60 kN 135 RPM 60 kN 137 RPM

60 kN 178 RPM 60 kN 195 RPM

60 kN 297 RPM 60 kN 375 RPM

75 kN 48 RPM 75 kN 124 RPM

06

measured film thickness (mm)

Figure 14 Comparison of rolling-element-bearing macrlm thickness measured byan ultrasonic means with EHD theoretical solution

water bath machined out of the bearing bush The transducer was spherically focusedand positioned in the water bath so that the wave was focused on the contact betweena ball and the raceway The bearing was loaded hydraulically and rotated by anelectric motor The bearing cavity was regooded with a mineral oil (Shell Turbo T68) Athermocouple was positioned on the outer raceway near the ultrasonic measurementpoint The bearing was loaded to give a contact eclipse between the ball and theouter raceway of semi-major and semi-minor axes 115 and 08 mm respectivelyThe bearing was then rotated and the transducer set to continuously pulse at arepetition rate of 10 kHz

The focal spot size of the transducer was ca 500 mm The maximum rotationalspeed of the bearing in these tests was 375 rpm At this rotational speed theregion of focused ultrasound would remain completely within the lubricated con-tact for ca 05 ms This allowed approximately shyve discrete pulses of ultrasound tobe reregected from the lubricant shylm as each ball passed through the measurementzone Initially a reference reregected pulse was recorded when the bearing was station-ary and there was no ball located over the measurement zone (although the cavitywas still shylled with oil) If a pulse is incident on an EHD shylm its amplitude is reducedbecause part of the wave has been transmitted through the oil shylm into the ball Bycontinuously monitoring the signals reregected from the raceway measurements of theball-raceway contacts were made Of the shyve pulses reregected from the ball-racewaycontact the lowest amplitude pulse was selected for analysis This pulse correspondsto the thinnest measured shylm thickness It should be noted that the resolution of thefocused transducer and the measurement interval are such that it was not possibleto record the horseshoe-shaped minimum shylm-thickness constriction at the contactexit The selected pulse was analysed shyrstly using (53) to calculate the reregection

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 973

film

thic

knes

s (m

m)

1000

100

10

1

01

001

00010 10 20 30 40 50 60

f (MHz)

time of flight limit

resonance method limit

spring model upper limit (R = 09)

spring model lower limit (R = 01)

Figure 15 Limits of operation for macrlm-thickness measurement by ultrasonic means

coemacrcient and then using the spring model to predict the shylm thickness The speedof sound in the oil in the contact is set to c = 4400 m siexcl1 (determined using themethod described in x 3)

Figure 14 shows the measured shylm thickness plotted against a prediction of theshylm thickness from the solution for an elliptical contact of Dowson amp Higginson(1966) (equation (61)) The bearing and lubricant heats up during operation Thetemperature of the entrained oil was monitored and used to determine an appropriateviscosity with which to calculate the shylm thickness in (61) This was why the resultswere not plotted as shylm thickness against speed (as in shygure 11) because viscositywas varying throughout the test

The results in shygure 14 show good agreement between measured lubricant-shylmthickness and that predicted by the EHD regression equations The spread along thex-axis shows the variation in shylm for nominally the same bearing operating conditions(load speed and oil temperature) At this stage it is not clear whether this scatteris a result of the measurement process or whether this is the actual shylm thicknessin the bearing It is worth noting that this measurement process could be improvedif the exact position of the ball could be related to the ultrasonic measurement soallowing a more precise measurement of the minimum shylm thickness

7 Discussion limits of operation

It is instructive to consider the limits of shylm-thickness measurement for a given ultra-sonic frequency The simplest method for determining the thickness of a lubricantlayer providing it is sumacrciently thick is by measuring the ToF through the layerA reregection occurs at the layer front face and another at the back face The thick-ness is readily obtained from the time between the arrival of these pulses multipliedby the acoustic velocity For the method to work the two reregected pulses must besumacrciently discrete and so the propagation distance must be greater than the pulse

Proc R Soc Lond A (2003)

974 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

width and so the minimum shylm thickness detectable by this method is given by

h gtnc

2f (71)

where n is the number of wavelengths in the ultrasonic pulse typically around threeThis measurement limit is plotted in shygure 15 as the minimum frequency requiredto measure a given shylm thickness Conventional ultrasonic non-destructive testingis generally restricted by losses in the propagating media (steel in this case) tofrequencies below 4060 MHz From (71) this means that the ToF method is onlypractically useful for layers of thickness greater than 40 mm This is thicker than thatfound on most commercial bearing systems

A lubricant layer resonates at a frequency given by (23) This equation also givesthe low thickness limit for this technique as the upper frequency output by a giventransducer determined the lowest measurable layer thickness This limit is also shownin shygure 15 for the shyrst through-thickness mode (ie m = 1) So using the highestpractical frequencies shylms greater than 10 mm are measurable by the shylm-resonancemethod

The upper limit of shylm thickness measurable using the spring-model approach isreached as R tends to unity in (27) Experience shows that measurements of R lessthan 09 yield satisfactory results The lowest shylm thickness measurable will dependon the smallest possible value of R This in turn will depend on the signal-to-noiseratio A signal-to-noise ratio of 60 dB is typical for conventional ultrasonic non-destructive testing systems The noise amplitude is thus 1

1000of the pulse amplitude

In the case of a measurement on a real bearing the achievable signal-to-noise ratiowill be reduced by the transducer-bearing reregection coemacrcient and by the attenuationin the bearing shell This means that the pulse incident in the reguid shylm will bereduced from that output by the transducer by a factor of shyve (as a conservativeestimate) Further it is assumed that for reliable measurements a pulse reregectedfrom the oil layer should have an amplitude approximately 20 times that of the noiselevel This results in a minimum measurable reregection coemacrcient of R = 01 Therelationships between the shylm thickness and the transducer frequency for the upperlimit when R = 09 and the lower where R = 01 are shown in shygure 15

This indicates that for a measuring frequency of 60 MHz a lubricant shylm of 2 nmis measurable This opens up the possibility of measuring boundary-type lubricantshylms between machine elements However the models presented here are designedfor a parallel-sided oil layer completely separating the smooth bearing surface If atthese low shylm thickness metal-to-metal contact occurs then transmission will occurat this location In this case some alternative method for interpreting reregectioncoemacrcients will be needed

8 Conclusions

Ultrasound is reregected from the lubricant shylm between bearing surfaces It is possibleto deduce the thickness of the lubricant shylm by comparing the frequency spectrumof the reregected pulse with that of the incident pulse The response of the lubricantlayer to an ultrasonic pulse has been modelled using both a spring-model methodand a continuum method The spring model is suitable for thin lubricant shylms inwhich the wavelength of the ultrasound is much larger than the layer thickness The

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 975

continuum model is valid for all layer thicknesses and allows the prediction of thethrough-thickness resonant frequencies of the lubricant layers Measurement of thesethrough-thickness resonances also provides a means of measuring the layer thickness

Experiments on reguid layers between regat plates and eccentric rings have demon-strated that ultrasound can suitably measure a wide range of liquid layer thicknessThe EHD lubricant shylm that forms between a ball sliding on a regat surface hasalso been measured ultrasonically The measured results agree well with theoreti-cal predictions taking into account the greatly increased speed of sound throughthe lubricant when it is under high pressure Films in the range 50500 nm wererecorded

The approach can also be used to measure shylm thickness in a rolling-elementbearing An ultrasonic transducer was mounted on the bearing raceway and thepulse reregected from the lubricant layer generated as the ball passes was recordedAgain measured results agreed well with theoretical predictions

The lower limit of measurement by this method depends on the signal-to-noiseratio A continuum model showed that using frequencies up to 60 MHz permits themeasurement of 2 nm thick shylms There is no upper limit to shylm-thickness measure-ment Thick shylms (greater than 40 mm) can be measured by a time-of-regight methodFilms of intermediate thickness can be determined by measuring the frequency atwhich the shylm resonates

This work was funded by a grant from the UK Engineering and Physical Sciences ResearchCouncil under the ROPA programme The authors acknowledge the help of Phil Harper of theUniversity of Sheplusmneld for his assistance with some of the measurements

References

Astridge D G amp Longmacreld M D 1967 Capacitance measurement and oil macrlm thickness in alarge radius disc and ring machine Proc Inst Mech Engrs 182 8996

Cameron A amp Gohar R 1966 Theoretical and experimental studies of the oil macrlm in lubricatedpoint contact Proc R Soc Lond A 291 520536

Dowson D amp Higginson G R 1966 Elastohydrodynamic lubrication|the fundamentals of roller

and gear lubrication Oxford Pergamon

Drinkwater B W Dwyer-Joyce R S amp Cawley P 1996 A study of the interaction betweenultrasound and a partially contacting solidsolid interface Proc R Soc Lond A 452 26132628

El-Sisi S I amp Shawki G S A 1960 Measurement of oil-macrlm thickness between disks by electricalconductivity Trans ASME J Basic Engng 82 12

Hamilton G M amp Moore S L 1967 A modimacred gauge for investigating an elastohydrodynamiccontact Proc Inst Mech Engrs 182 251

Hamrock B J 1994 Fundamentals of deguid macrlm lubrication McGraw-Hill

Hosten B 1991 Bulk heterogeneous plane-wave propagation through viscoelastic plates andstratimacred media with large values of frequency-domain Ultrasonics 29 445450

Jacobson B O amp Vinet P 1987 A model for the indeguence of pressure on the bulk modulusand the indeguence of temperature on the solidimacrcation pressure for liquid lubricants Trans

ASME J Tribology 109 709

Johnston G J Wayte R amp Spikes H A 1991 The measurement and study of very thinlubricant macrlms in concentrated contacts Tribol Trans 34 187194

Kinra V K Jaminet P T Zhu C amp Iyer V R 1994 Simultaneous measurement of theacoustical properties of a thin-layered medium the inverse problem J Acoust Soc Am 9530593074

Proc R Soc Lond A (2003)

964 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

ball bearing

raceway

focusedultrasonictransducer

lubricant film

controlsignal

digital scope

downloadwaveform to PC

UPR

PC

Figure 4 Schematic of ultrasonic pulsing and receiving system

transducer

water tank

shim

glasssheets

positioning scale

Figure 5 Schematic of the apparatus used for generatingthin liquid macrlms between two degat surfaces

5 Measurement of a stationary liquid layer

Initial experiments were performed on thin liquid layers between stationary solidsurfaces Two conshygurations were chosen a water wedge between optical glass regatsand an oil shylm between two eccentric cylinders The former apparatus was used toproduce a wide range of measurable liquid-layer thickness The latter was designed toinvestigate the enotects of the curvature of the solid surfaces and the use of a mineraloil as the liquid medium

(a) Liquid-wedge apparatus

Shims of various thickness were used to separate sheets of regoat glass which werethen immersed in a water tank as shown in shygure 5 The ultrasonic transducerswere also immersed in the water tank and mounted above the liquid wedge on acomputer-controlled xy positioning frame The ultrasonic pulsing and receiving wascontrolled by the apparatus as shown in shygure 4

The shyrst step in the procedure was to determine the frequency characteristics of theincident ultrasonic pulse The bottom glass plate was removed and the pulse reregected

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 965

6 7 8 9 10 11

10

09

08

07

06

05

04

03

02

refl

ect

ion c

oef

fici

ent

18 mm

53 mm

89 mm

124 mm

159 mm

195 mm

(a)

10

08

06

04

02

0

refl

ect

ion c

oeff

icie

nt

15 17 19 21 23 25 27 29 31 33

f (MHz)

125 mm 375 mm 50 mm 625 mm 75 mm(b)

Figure 6 Measured redegection-coeplusmncient spectra for a range of deguid macrlm thicknesses using(a) a 10 MHz and (b) a 25 MHz centre-frequency transducer

from the glasswater interface recorded This time-domain signal was converted tothe frequency domain via a fast Fourier transform and stored as a reference Aref Inthis way

Aref(f) = I(f)Rgw (51)

where I(f ) is the frequency-response characteristic of the incident pulse and Rgw

is the glasswater reregection coemacrcient given by (21) The bottom plate was thenrepositioned and measurements of the pulse reregected from the reguid shylm were recordedat various locations along the reguid wedge This measurement signal Am eas can bewritten as

Am eas (f) = I(f)Rl(f) (52)

Proc R Soc Lond A (2003)

966 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

25

20

15

10

5

0

film

thic

knes

s (m

m)

60 65 70 75 80 85 90 95 100 105 110

f (MHz)

Figure 7 Film-thickness results determined by the application ofthe spring model to the redegection spectra of macrgure 6a

where Rl(f) is the reregection-coemacrcient spectrum of the lubricant layer which canthen be obtained by combining (51) and (52)

Rl(f) =Am eas (f)

Aref(f)Rgw (53)

Figure 6 shows two sets of reregection-coemacrcient spectra of liquid layers in a liquid-wedge experiment recorded using two dinoterent wide-band transducers for a rangeof shylm thickness The thickness of the liquid layer at any measuring location wasestimated from the geometry of the reguid wedge formed by the shim

From shygure 6b it can be seen that at higher shylm thicknesses resonant frequencies(observed as minima in the reregection-coemacrcient spectra) are visible When these res-onances occur the layer thickness can be readily determined from (23) For thinnerliquid layers andor when using lower-frequency transducers the resonance is notobserved as it occurs beyond the frequency range of the transducer However theshape of the reregection-coemacrcient spectrum below resonance can be used to predictthe thickness of the liquid layer though the application of the spring model (equa-tion (27))

The stinotness of the layer can be measured over a range of frequencies with onetransducer As the stinotness at a single frequency is sumacrcient to enable prediction ofthe reguid-layer thickness there is some redundancy in the data that can be used as amethod of checking the accuracy of the spring model Figure 7 shows the data given inshygure 6a converted to shylm thickness via (27) over the bandwidth of the transducerFrom shygure 7 it can be seen that for the lower shylm-thickness values the curvesare horizontal This indicates a good measurement as the shylm thickness cannot bea function of the frequency with which it is measured However for the top curvethe model does not correctly convert the reregection coemacrcient to a constant layerthickness This is because as the reregection coemacrcient tends to unity so the springmodel (equation (27)) becomes prone to numerical error For the next curve down

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 967

0

10

20

30

40

50

70

mea

sure

d f

ilm

thic

kness

(m

m)

60

predicted film thickness (mm)

10 20 30 40 50 60 70

Figure 8 Film-thickness values measured by ultrasonic redegection compared withpredictions of the thickness determined from the geometry of the deguid wedge

at the higher frequencies the same happens This represents a limit of the spring-model approach and to measure these thicker shylms either lower frequencies shouldbe used so R is lower or higher frequencies used and the location of resonancesdetermined

Figure 8 shows ultrasonic measurements of the thickness of the liquid shylm com-pared with the geometrical prediction of the layer thickness The data below 25 mmcorrespond to measurements performed using the spring model while the data above25 mm have been determined from the measurement of shylm resonances Agreementis good (and a straight line is observed) but in practice the measured liquid-layerthickness tends to be slightly larger than that of the shim This is likely to becaused by either some thin residual of water between the shim of the glass plateor by deformation of the shim where it has been cut Each of these enotects wouldtend to make the liquid layer thicker and hence explain the dinoterence seen in shyg-ure 8

(b) Annular oil-macrlm apparatus

Figure 9 shows the apparatus to create an oil wedge between a ring and a shaft Thering and shaft were made from aluminium The ringshaft interface had a nominaldiameter of 70 mm and a diametral clearance of 100 mm The shaft was spring loadedagainst the ring By changing the position of the loading point the gap thicknessin the region above the transducer could be varied The gap was shylled with mineraloil (Shell Turbo T68) through a small shyller hole A 25 MHz focused transducer waslocated in a water bath beneath the assembly The transducer was positioned so thatthe wave was focused on the reguid layer

Figure 10 shows a plot of the shylm thickness determined from the reregection mea-surements for various angular positions of the loading point relative to the ultra-sonic measurement position In this case all the shylms were measured using theshylm-resonance method The theoretical width of annular gap h between eccentriccylinders is obtained from geometry

h = R1

middot

1 iexcl

micro

R1 iexcl R2

R1

para2

sin2 iquest

cedil1=2

iexcl R2 + (R1 iexcl R2) cos iquest (54)

Proc R Soc Lond A (2003)

968 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

transducer

water tank

measurement zone

oil-filled annulus

tension spring

aluminium cylinders

Figure 9 Apparatus used to create an annular oil macrlm for ultrasonic-redegection experiments

film

thic

knes

s (m

m)

100

90

80

70

60

50

40

30

20

10

0

angular position (deg)

-180 -135 -90 -45 0 45 90 135 180

ultrasonic measurements

mathematical solution

Figure 10 Film-thickness values measured by ultrasonic redegection for an annular macrlm betweentwo eccentric cylinders Experimental results are compared with the geometrical solution

where R1 and R2 are the radii of the bush and shaft respectively and rsquo is theangle measured from the point of contact Equation (54) is included in shygure 10 forcomparison and a good correlation was observed

To reduce the enotects of the curvature of the lubricated interface the transducersused in this experiment focus the wave onto the oil layer The spot size of the focusedwave varies with frequency according to the relationship (Silk 1984)

df(iexcl6 d B) =1028F c

fD (55)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 969

steel disc water bath

oil meniscus

rotating steel ball

transducer

hydraulic load

motor drive

Figure 11 Schematic of the experimental apparatus used to generatean EHD macrlm for a ball sliding on a degat

where df is the diameter of the spot size (where the signal has reduced to iexcl6 dBof its peak value) F is the transducer focusing length f is the wave frequencyc is the speed of sound in water and D is the diameter of the piezoelectric elementFor a 25 MHz frequency wave this corresponds to a spot size in water of 522 mmThis is small compared with the radius of the shaftbush apparatus So essentiallythe transducer is receiving signals back from a regat region of constant shylm thick-ness and the curvature has little enotect The good agreement between experimen-tal and theoretical liquid-layer thickness shown in shygure 10 further validates thishypothesis

6 Measurement of dynamic lubricating macrlms

An EHD lubricant shylm forms between rolling or sliding non-conformal contactsTypically the thickness of the oil layer is in the region of 011 mm This is withinthe range of the possible measurement by ultrasonic means and within the spring-model regime of ultrasonic response In this work EHD shylms have been measuredin a model rig containing a single stationary lubricated contact and in a rolling-element bearing where the lubricant shylm is transient (with respect to the trans-ducer)

(a) Ball on disc EHD lubrication apparatus

Figure 11 shows the apparatus used to generate a single EHD lubricated contactA steel ball is supported on rollers and hydraulically loaded onto the underside ofa steel disc The ball is rotated at constant speed by an electric motor througha gear box and quill shaft The steel disc is held stationary such that the ball iscompletely sliding against the underside of the disc This apparatus is a modishyed`optical elastohydrodynamicrsquo apparatus (originally developed by Cameron amp Gohar(1966)) where the semi-reregective rotating glass disc has been replaced by a station-

Proc R Soc Lond A (2003)

970 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

005

010

015

020

025

030

035

040

0 02 04 06 08 10 12 14

lubri

can

t fi

lm thic

kness

(m

m)

entrainment speed (m s-1)

theoretical solution a = 015 mmmeasurements a = 015 mmtheoretical solution a = 01 mmmeasurements a = 01 mm

Figure 12 EHD lubricant-macrlm-thickness variation with ball-sliding speed for two loadsUltrasonic-redegection measurements are compared with a theoretical solution

ary steel disc and the microscope replaced by an ultrasonic transducer The balldisc contact was regooded with a mineral oil (Shell Turbo T68) which is entrainedinto the contact to form an EHD shylm A 50 MHz focused transducer was mountedabove the contact in a water bath The transducer was positioned directly abovethe contact region and at a distance such that the wave is focused on the balldiscinterface

Reregected pulses were recorded from the discball interface as the ball rotationalspeed and load were varied A reference spectrum was obtained by recording the pulsereregected when the ball was out of contact with the disc but the disc was still regoodedwith oil As in the wedge experiment the reference and lubricant-layer measurementswere used in (32) to obtain the reregection-coemacrcient spectrum of the lubricant layerA series of reregection coemacrcient spectra were then recorded from the discball contactas the sliding speed was increased The spring model (equation (27)) was used todetermine the shylm thickness from these spectra An automated LabView interfacewas written to record the spectra divide by a reference and convert the data intoshylm thickness (as shown in shygure 6) As discussed in x 3 above the density and speedof sound of the oil used in (27) are those at contact pressure (in this case 08 GPa)and not those in the bulk

Figure 12 shows the measured variation in shylm thickness determined from thereregection coemacrcient spectra as the speed is increased for two load cases (giving con-tact radii a of 01 and 015 mm) For this lubrication case a theoretical predictionof the oil-shylm thickness can be obtained from the regression equations of Dowson ampHigginson (1966) The central shylm thickness hc is expressed as a regression equationconsisting of shyve non-dimensional parameters

Hc = 269U 067G053W iexcl0067(1 iexcl 061eiexcl073k) (61)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 971

test rolling bearing

measurement zone

hydraulic loading

focusing transducer

water bath

belt and pulley drive

Figure 13 Schematic of apparatus used for ultrasonic measurementsof macrlm thickness in rolling-element bearings

where

Hc =hc

Rx

W =P

2EcurrenR2x

U =sup20u

2EcurrenRx

k = 103

micro

Ry

Rx

para064

G = 2notEcurren

where Ecurren is the reduced modulus Rx and Ry are the reduced radii in the paralleland transverse directions u is the mean surface speed P is the applied contact loadsup20 is the viscosity of oil in the inlet and not is its pressure-viscosity coemacrcient

The predictions of (61) for the two load cases are plotted in shygure 12 The agree-ment between the theoretical solution and the experimental data is good Typicallythe measured data are repeatable to within sect20 The oil shylm generated by theapparatus is not completely stable To directly observe the lubricant shylm the steeldisc was replaced by the glass disc and the shylm monitored visually A certain amountof shylm reguctuation was observed during normal running (caused by a slight processingof the ball on its supporting rollers) Notwithstanding the results are encouragingbecause this indicates that both the integrity of the ultrasonic method and alsothat the speed of sound of the lubricating oil compares well with predictions fromhigh-pressure measurements

(b) Rolling bearing lubricant-macrlm measurement

The duration of the ultrasonic pulses used in this work was short Spatially thepulse width was typically three wavelengths in length A 25 MHz wave travelling insteel results in a pulse duration of 01 ms Therefore it is feasible to record the shylmthickness in a rolling element moving past the focal point of an ultrasonic transducer

The approach has been used to measure shylm thickness in a 6410 deep-grooveball bearing Figure 13 shows a schematic of the bearing and the positioning of thetransducer The 25 MHz transducer (see table 2 for details) was located in a small

Proc R Soc Lond A (2003)

972 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

0

01

02

03

04

05

07

01 02 03 04 05 06 07

theo

reti

cal

film

thic

knes

s pre

dic

tion (

mm

)

45 kN 112 RPM 60 kN 72 RPM

60 kN 103 RPM 60 kN 128 RPM

60 kN 135 RPM 60 kN 137 RPM

60 kN 178 RPM 60 kN 195 RPM

60 kN 297 RPM 60 kN 375 RPM

75 kN 48 RPM 75 kN 124 RPM

06

measured film thickness (mm)

Figure 14 Comparison of rolling-element-bearing macrlm thickness measured byan ultrasonic means with EHD theoretical solution

water bath machined out of the bearing bush The transducer was spherically focusedand positioned in the water bath so that the wave was focused on the contact betweena ball and the raceway The bearing was loaded hydraulically and rotated by anelectric motor The bearing cavity was regooded with a mineral oil (Shell Turbo T68) Athermocouple was positioned on the outer raceway near the ultrasonic measurementpoint The bearing was loaded to give a contact eclipse between the ball and theouter raceway of semi-major and semi-minor axes 115 and 08 mm respectivelyThe bearing was then rotated and the transducer set to continuously pulse at arepetition rate of 10 kHz

The focal spot size of the transducer was ca 500 mm The maximum rotationalspeed of the bearing in these tests was 375 rpm At this rotational speed theregion of focused ultrasound would remain completely within the lubricated con-tact for ca 05 ms This allowed approximately shyve discrete pulses of ultrasound tobe reregected from the lubricant shylm as each ball passed through the measurementzone Initially a reference reregected pulse was recorded when the bearing was station-ary and there was no ball located over the measurement zone (although the cavitywas still shylled with oil) If a pulse is incident on an EHD shylm its amplitude is reducedbecause part of the wave has been transmitted through the oil shylm into the ball Bycontinuously monitoring the signals reregected from the raceway measurements of theball-raceway contacts were made Of the shyve pulses reregected from the ball-racewaycontact the lowest amplitude pulse was selected for analysis This pulse correspondsto the thinnest measured shylm thickness It should be noted that the resolution of thefocused transducer and the measurement interval are such that it was not possibleto record the horseshoe-shaped minimum shylm-thickness constriction at the contactexit The selected pulse was analysed shyrstly using (53) to calculate the reregection

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 973

film

thic

knes

s (m

m)

1000

100

10

1

01

001

00010 10 20 30 40 50 60

f (MHz)

time of flight limit

resonance method limit

spring model upper limit (R = 09)

spring model lower limit (R = 01)

Figure 15 Limits of operation for macrlm-thickness measurement by ultrasonic means

coemacrcient and then using the spring model to predict the shylm thickness The speedof sound in the oil in the contact is set to c = 4400 m siexcl1 (determined using themethod described in x 3)

Figure 14 shows the measured shylm thickness plotted against a prediction of theshylm thickness from the solution for an elliptical contact of Dowson amp Higginson(1966) (equation (61)) The bearing and lubricant heats up during operation Thetemperature of the entrained oil was monitored and used to determine an appropriateviscosity with which to calculate the shylm thickness in (61) This was why the resultswere not plotted as shylm thickness against speed (as in shygure 11) because viscositywas varying throughout the test

The results in shygure 14 show good agreement between measured lubricant-shylmthickness and that predicted by the EHD regression equations The spread along thex-axis shows the variation in shylm for nominally the same bearing operating conditions(load speed and oil temperature) At this stage it is not clear whether this scatteris a result of the measurement process or whether this is the actual shylm thicknessin the bearing It is worth noting that this measurement process could be improvedif the exact position of the ball could be related to the ultrasonic measurement soallowing a more precise measurement of the minimum shylm thickness

7 Discussion limits of operation

It is instructive to consider the limits of shylm-thickness measurement for a given ultra-sonic frequency The simplest method for determining the thickness of a lubricantlayer providing it is sumacrciently thick is by measuring the ToF through the layerA reregection occurs at the layer front face and another at the back face The thick-ness is readily obtained from the time between the arrival of these pulses multipliedby the acoustic velocity For the method to work the two reregected pulses must besumacrciently discrete and so the propagation distance must be greater than the pulse

Proc R Soc Lond A (2003)

974 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

width and so the minimum shylm thickness detectable by this method is given by

h gtnc

2f (71)

where n is the number of wavelengths in the ultrasonic pulse typically around threeThis measurement limit is plotted in shygure 15 as the minimum frequency requiredto measure a given shylm thickness Conventional ultrasonic non-destructive testingis generally restricted by losses in the propagating media (steel in this case) tofrequencies below 4060 MHz From (71) this means that the ToF method is onlypractically useful for layers of thickness greater than 40 mm This is thicker than thatfound on most commercial bearing systems

A lubricant layer resonates at a frequency given by (23) This equation also givesthe low thickness limit for this technique as the upper frequency output by a giventransducer determined the lowest measurable layer thickness This limit is also shownin shygure 15 for the shyrst through-thickness mode (ie m = 1) So using the highestpractical frequencies shylms greater than 10 mm are measurable by the shylm-resonancemethod

The upper limit of shylm thickness measurable using the spring-model approach isreached as R tends to unity in (27) Experience shows that measurements of R lessthan 09 yield satisfactory results The lowest shylm thickness measurable will dependon the smallest possible value of R This in turn will depend on the signal-to-noiseratio A signal-to-noise ratio of 60 dB is typical for conventional ultrasonic non-destructive testing systems The noise amplitude is thus 1

1000of the pulse amplitude

In the case of a measurement on a real bearing the achievable signal-to-noise ratiowill be reduced by the transducer-bearing reregection coemacrcient and by the attenuationin the bearing shell This means that the pulse incident in the reguid shylm will bereduced from that output by the transducer by a factor of shyve (as a conservativeestimate) Further it is assumed that for reliable measurements a pulse reregectedfrom the oil layer should have an amplitude approximately 20 times that of the noiselevel This results in a minimum measurable reregection coemacrcient of R = 01 Therelationships between the shylm thickness and the transducer frequency for the upperlimit when R = 09 and the lower where R = 01 are shown in shygure 15

This indicates that for a measuring frequency of 60 MHz a lubricant shylm of 2 nmis measurable This opens up the possibility of measuring boundary-type lubricantshylms between machine elements However the models presented here are designedfor a parallel-sided oil layer completely separating the smooth bearing surface If atthese low shylm thickness metal-to-metal contact occurs then transmission will occurat this location In this case some alternative method for interpreting reregectioncoemacrcients will be needed

8 Conclusions

Ultrasound is reregected from the lubricant shylm between bearing surfaces It is possibleto deduce the thickness of the lubricant shylm by comparing the frequency spectrumof the reregected pulse with that of the incident pulse The response of the lubricantlayer to an ultrasonic pulse has been modelled using both a spring-model methodand a continuum method The spring model is suitable for thin lubricant shylms inwhich the wavelength of the ultrasound is much larger than the layer thickness The

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 975

continuum model is valid for all layer thicknesses and allows the prediction of thethrough-thickness resonant frequencies of the lubricant layers Measurement of thesethrough-thickness resonances also provides a means of measuring the layer thickness

Experiments on reguid layers between regat plates and eccentric rings have demon-strated that ultrasound can suitably measure a wide range of liquid layer thicknessThe EHD lubricant shylm that forms between a ball sliding on a regat surface hasalso been measured ultrasonically The measured results agree well with theoreti-cal predictions taking into account the greatly increased speed of sound throughthe lubricant when it is under high pressure Films in the range 50500 nm wererecorded

The approach can also be used to measure shylm thickness in a rolling-elementbearing An ultrasonic transducer was mounted on the bearing raceway and thepulse reregected from the lubricant layer generated as the ball passes was recordedAgain measured results agreed well with theoretical predictions

The lower limit of measurement by this method depends on the signal-to-noiseratio A continuum model showed that using frequencies up to 60 MHz permits themeasurement of 2 nm thick shylms There is no upper limit to shylm-thickness measure-ment Thick shylms (greater than 40 mm) can be measured by a time-of-regight methodFilms of intermediate thickness can be determined by measuring the frequency atwhich the shylm resonates

This work was funded by a grant from the UK Engineering and Physical Sciences ResearchCouncil under the ROPA programme The authors acknowledge the help of Phil Harper of theUniversity of Sheplusmneld for his assistance with some of the measurements

References

Astridge D G amp Longmacreld M D 1967 Capacitance measurement and oil macrlm thickness in alarge radius disc and ring machine Proc Inst Mech Engrs 182 8996

Cameron A amp Gohar R 1966 Theoretical and experimental studies of the oil macrlm in lubricatedpoint contact Proc R Soc Lond A 291 520536

Dowson D amp Higginson G R 1966 Elastohydrodynamic lubrication|the fundamentals of roller

and gear lubrication Oxford Pergamon

Drinkwater B W Dwyer-Joyce R S amp Cawley P 1996 A study of the interaction betweenultrasound and a partially contacting solidsolid interface Proc R Soc Lond A 452 26132628

El-Sisi S I amp Shawki G S A 1960 Measurement of oil-macrlm thickness between disks by electricalconductivity Trans ASME J Basic Engng 82 12

Hamilton G M amp Moore S L 1967 A modimacred gauge for investigating an elastohydrodynamiccontact Proc Inst Mech Engrs 182 251

Hamrock B J 1994 Fundamentals of deguid macrlm lubrication McGraw-Hill

Hosten B 1991 Bulk heterogeneous plane-wave propagation through viscoelastic plates andstratimacred media with large values of frequency-domain Ultrasonics 29 445450

Jacobson B O amp Vinet P 1987 A model for the indeguence of pressure on the bulk modulusand the indeguence of temperature on the solidimacrcation pressure for liquid lubricants Trans

ASME J Tribology 109 709

Johnston G J Wayte R amp Spikes H A 1991 The measurement and study of very thinlubricant macrlms in concentrated contacts Tribol Trans 34 187194

Kinra V K Jaminet P T Zhu C amp Iyer V R 1994 Simultaneous measurement of theacoustical properties of a thin-layered medium the inverse problem J Acoust Soc Am 9530593074

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 965

6 7 8 9 10 11

10

09

08

07

06

05

04

03

02

refl

ect

ion c

oef

fici

ent

18 mm

53 mm

89 mm

124 mm

159 mm

195 mm

(a)

10

08

06

04

02

0

refl

ect

ion c

oeff

icie

nt

15 17 19 21 23 25 27 29 31 33

f (MHz)

125 mm 375 mm 50 mm 625 mm 75 mm(b)

Figure 6 Measured redegection-coeplusmncient spectra for a range of deguid macrlm thicknesses using(a) a 10 MHz and (b) a 25 MHz centre-frequency transducer

from the glasswater interface recorded This time-domain signal was converted tothe frequency domain via a fast Fourier transform and stored as a reference Aref Inthis way

Aref(f) = I(f)Rgw (51)

where I(f ) is the frequency-response characteristic of the incident pulse and Rgw

is the glasswater reregection coemacrcient given by (21) The bottom plate was thenrepositioned and measurements of the pulse reregected from the reguid shylm were recordedat various locations along the reguid wedge This measurement signal Am eas can bewritten as

Am eas (f) = I(f)Rl(f) (52)

Proc R Soc Lond A (2003)

966 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

25

20

15

10

5

0

film

thic

knes

s (m

m)

60 65 70 75 80 85 90 95 100 105 110

f (MHz)

Figure 7 Film-thickness results determined by the application ofthe spring model to the redegection spectra of macrgure 6a

where Rl(f) is the reregection-coemacrcient spectrum of the lubricant layer which canthen be obtained by combining (51) and (52)

Rl(f) =Am eas (f)

Aref(f)Rgw (53)

Figure 6 shows two sets of reregection-coemacrcient spectra of liquid layers in a liquid-wedge experiment recorded using two dinoterent wide-band transducers for a rangeof shylm thickness The thickness of the liquid layer at any measuring location wasestimated from the geometry of the reguid wedge formed by the shim

From shygure 6b it can be seen that at higher shylm thicknesses resonant frequencies(observed as minima in the reregection-coemacrcient spectra) are visible When these res-onances occur the layer thickness can be readily determined from (23) For thinnerliquid layers andor when using lower-frequency transducers the resonance is notobserved as it occurs beyond the frequency range of the transducer However theshape of the reregection-coemacrcient spectrum below resonance can be used to predictthe thickness of the liquid layer though the application of the spring model (equa-tion (27))

The stinotness of the layer can be measured over a range of frequencies with onetransducer As the stinotness at a single frequency is sumacrcient to enable prediction ofthe reguid-layer thickness there is some redundancy in the data that can be used as amethod of checking the accuracy of the spring model Figure 7 shows the data given inshygure 6a converted to shylm thickness via (27) over the bandwidth of the transducerFrom shygure 7 it can be seen that for the lower shylm-thickness values the curvesare horizontal This indicates a good measurement as the shylm thickness cannot bea function of the frequency with which it is measured However for the top curvethe model does not correctly convert the reregection coemacrcient to a constant layerthickness This is because as the reregection coemacrcient tends to unity so the springmodel (equation (27)) becomes prone to numerical error For the next curve down

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 967

0

10

20

30

40

50

70

mea

sure

d f

ilm

thic

kness

(m

m)

60

predicted film thickness (mm)

10 20 30 40 50 60 70

Figure 8 Film-thickness values measured by ultrasonic redegection compared withpredictions of the thickness determined from the geometry of the deguid wedge

at the higher frequencies the same happens This represents a limit of the spring-model approach and to measure these thicker shylms either lower frequencies shouldbe used so R is lower or higher frequencies used and the location of resonancesdetermined

Figure 8 shows ultrasonic measurements of the thickness of the liquid shylm com-pared with the geometrical prediction of the layer thickness The data below 25 mmcorrespond to measurements performed using the spring model while the data above25 mm have been determined from the measurement of shylm resonances Agreementis good (and a straight line is observed) but in practice the measured liquid-layerthickness tends to be slightly larger than that of the shim This is likely to becaused by either some thin residual of water between the shim of the glass plateor by deformation of the shim where it has been cut Each of these enotects wouldtend to make the liquid layer thicker and hence explain the dinoterence seen in shyg-ure 8

(b) Annular oil-macrlm apparatus

Figure 9 shows the apparatus to create an oil wedge between a ring and a shaft Thering and shaft were made from aluminium The ringshaft interface had a nominaldiameter of 70 mm and a diametral clearance of 100 mm The shaft was spring loadedagainst the ring By changing the position of the loading point the gap thicknessin the region above the transducer could be varied The gap was shylled with mineraloil (Shell Turbo T68) through a small shyller hole A 25 MHz focused transducer waslocated in a water bath beneath the assembly The transducer was positioned so thatthe wave was focused on the reguid layer

Figure 10 shows a plot of the shylm thickness determined from the reregection mea-surements for various angular positions of the loading point relative to the ultra-sonic measurement position In this case all the shylms were measured using theshylm-resonance method The theoretical width of annular gap h between eccentriccylinders is obtained from geometry

h = R1

middot

1 iexcl

micro

R1 iexcl R2

R1

para2

sin2 iquest

cedil1=2

iexcl R2 + (R1 iexcl R2) cos iquest (54)

Proc R Soc Lond A (2003)

968 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

transducer

water tank

measurement zone

oil-filled annulus

tension spring

aluminium cylinders

Figure 9 Apparatus used to create an annular oil macrlm for ultrasonic-redegection experiments

film

thic

knes

s (m

m)

100

90

80

70

60

50

40

30

20

10

0

angular position (deg)

-180 -135 -90 -45 0 45 90 135 180

ultrasonic measurements

mathematical solution

Figure 10 Film-thickness values measured by ultrasonic redegection for an annular macrlm betweentwo eccentric cylinders Experimental results are compared with the geometrical solution

where R1 and R2 are the radii of the bush and shaft respectively and rsquo is theangle measured from the point of contact Equation (54) is included in shygure 10 forcomparison and a good correlation was observed

To reduce the enotects of the curvature of the lubricated interface the transducersused in this experiment focus the wave onto the oil layer The spot size of the focusedwave varies with frequency according to the relationship (Silk 1984)

df(iexcl6 d B) =1028F c

fD (55)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 969

steel disc water bath

oil meniscus

rotating steel ball

transducer

hydraulic load

motor drive

Figure 11 Schematic of the experimental apparatus used to generatean EHD macrlm for a ball sliding on a degat

where df is the diameter of the spot size (where the signal has reduced to iexcl6 dBof its peak value) F is the transducer focusing length f is the wave frequencyc is the speed of sound in water and D is the diameter of the piezoelectric elementFor a 25 MHz frequency wave this corresponds to a spot size in water of 522 mmThis is small compared with the radius of the shaftbush apparatus So essentiallythe transducer is receiving signals back from a regat region of constant shylm thick-ness and the curvature has little enotect The good agreement between experimen-tal and theoretical liquid-layer thickness shown in shygure 10 further validates thishypothesis

6 Measurement of dynamic lubricating macrlms

An EHD lubricant shylm forms between rolling or sliding non-conformal contactsTypically the thickness of the oil layer is in the region of 011 mm This is withinthe range of the possible measurement by ultrasonic means and within the spring-model regime of ultrasonic response In this work EHD shylms have been measuredin a model rig containing a single stationary lubricated contact and in a rolling-element bearing where the lubricant shylm is transient (with respect to the trans-ducer)

(a) Ball on disc EHD lubrication apparatus

Figure 11 shows the apparatus used to generate a single EHD lubricated contactA steel ball is supported on rollers and hydraulically loaded onto the underside ofa steel disc The ball is rotated at constant speed by an electric motor througha gear box and quill shaft The steel disc is held stationary such that the ball iscompletely sliding against the underside of the disc This apparatus is a modishyed`optical elastohydrodynamicrsquo apparatus (originally developed by Cameron amp Gohar(1966)) where the semi-reregective rotating glass disc has been replaced by a station-

Proc R Soc Lond A (2003)

970 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

005

010

015

020

025

030

035

040

0 02 04 06 08 10 12 14

lubri

can

t fi

lm thic

kness

(m

m)

entrainment speed (m s-1)

theoretical solution a = 015 mmmeasurements a = 015 mmtheoretical solution a = 01 mmmeasurements a = 01 mm

Figure 12 EHD lubricant-macrlm-thickness variation with ball-sliding speed for two loadsUltrasonic-redegection measurements are compared with a theoretical solution

ary steel disc and the microscope replaced by an ultrasonic transducer The balldisc contact was regooded with a mineral oil (Shell Turbo T68) which is entrainedinto the contact to form an EHD shylm A 50 MHz focused transducer was mountedabove the contact in a water bath The transducer was positioned directly abovethe contact region and at a distance such that the wave is focused on the balldiscinterface

Reregected pulses were recorded from the discball interface as the ball rotationalspeed and load were varied A reference spectrum was obtained by recording the pulsereregected when the ball was out of contact with the disc but the disc was still regoodedwith oil As in the wedge experiment the reference and lubricant-layer measurementswere used in (32) to obtain the reregection-coemacrcient spectrum of the lubricant layerA series of reregection coemacrcient spectra were then recorded from the discball contactas the sliding speed was increased The spring model (equation (27)) was used todetermine the shylm thickness from these spectra An automated LabView interfacewas written to record the spectra divide by a reference and convert the data intoshylm thickness (as shown in shygure 6) As discussed in x 3 above the density and speedof sound of the oil used in (27) are those at contact pressure (in this case 08 GPa)and not those in the bulk

Figure 12 shows the measured variation in shylm thickness determined from thereregection coemacrcient spectra as the speed is increased for two load cases (giving con-tact radii a of 01 and 015 mm) For this lubrication case a theoretical predictionof the oil-shylm thickness can be obtained from the regression equations of Dowson ampHigginson (1966) The central shylm thickness hc is expressed as a regression equationconsisting of shyve non-dimensional parameters

Hc = 269U 067G053W iexcl0067(1 iexcl 061eiexcl073k) (61)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 971

test rolling bearing

measurement zone

hydraulic loading

focusing transducer

water bath

belt and pulley drive

Figure 13 Schematic of apparatus used for ultrasonic measurementsof macrlm thickness in rolling-element bearings

where

Hc =hc

Rx

W =P

2EcurrenR2x

U =sup20u

2EcurrenRx

k = 103

micro

Ry

Rx

para064

G = 2notEcurren

where Ecurren is the reduced modulus Rx and Ry are the reduced radii in the paralleland transverse directions u is the mean surface speed P is the applied contact loadsup20 is the viscosity of oil in the inlet and not is its pressure-viscosity coemacrcient

The predictions of (61) for the two load cases are plotted in shygure 12 The agree-ment between the theoretical solution and the experimental data is good Typicallythe measured data are repeatable to within sect20 The oil shylm generated by theapparatus is not completely stable To directly observe the lubricant shylm the steeldisc was replaced by the glass disc and the shylm monitored visually A certain amountof shylm reguctuation was observed during normal running (caused by a slight processingof the ball on its supporting rollers) Notwithstanding the results are encouragingbecause this indicates that both the integrity of the ultrasonic method and alsothat the speed of sound of the lubricating oil compares well with predictions fromhigh-pressure measurements

(b) Rolling bearing lubricant-macrlm measurement

The duration of the ultrasonic pulses used in this work was short Spatially thepulse width was typically three wavelengths in length A 25 MHz wave travelling insteel results in a pulse duration of 01 ms Therefore it is feasible to record the shylmthickness in a rolling element moving past the focal point of an ultrasonic transducer

The approach has been used to measure shylm thickness in a 6410 deep-grooveball bearing Figure 13 shows a schematic of the bearing and the positioning of thetransducer The 25 MHz transducer (see table 2 for details) was located in a small

Proc R Soc Lond A (2003)

972 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

0

01

02

03

04

05

07

01 02 03 04 05 06 07

theo

reti

cal

film

thic

knes

s pre

dic

tion (

mm

)

45 kN 112 RPM 60 kN 72 RPM

60 kN 103 RPM 60 kN 128 RPM

60 kN 135 RPM 60 kN 137 RPM

60 kN 178 RPM 60 kN 195 RPM

60 kN 297 RPM 60 kN 375 RPM

75 kN 48 RPM 75 kN 124 RPM

06

measured film thickness (mm)

Figure 14 Comparison of rolling-element-bearing macrlm thickness measured byan ultrasonic means with EHD theoretical solution

water bath machined out of the bearing bush The transducer was spherically focusedand positioned in the water bath so that the wave was focused on the contact betweena ball and the raceway The bearing was loaded hydraulically and rotated by anelectric motor The bearing cavity was regooded with a mineral oil (Shell Turbo T68) Athermocouple was positioned on the outer raceway near the ultrasonic measurementpoint The bearing was loaded to give a contact eclipse between the ball and theouter raceway of semi-major and semi-minor axes 115 and 08 mm respectivelyThe bearing was then rotated and the transducer set to continuously pulse at arepetition rate of 10 kHz

The focal spot size of the transducer was ca 500 mm The maximum rotationalspeed of the bearing in these tests was 375 rpm At this rotational speed theregion of focused ultrasound would remain completely within the lubricated con-tact for ca 05 ms This allowed approximately shyve discrete pulses of ultrasound tobe reregected from the lubricant shylm as each ball passed through the measurementzone Initially a reference reregected pulse was recorded when the bearing was station-ary and there was no ball located over the measurement zone (although the cavitywas still shylled with oil) If a pulse is incident on an EHD shylm its amplitude is reducedbecause part of the wave has been transmitted through the oil shylm into the ball Bycontinuously monitoring the signals reregected from the raceway measurements of theball-raceway contacts were made Of the shyve pulses reregected from the ball-racewaycontact the lowest amplitude pulse was selected for analysis This pulse correspondsto the thinnest measured shylm thickness It should be noted that the resolution of thefocused transducer and the measurement interval are such that it was not possibleto record the horseshoe-shaped minimum shylm-thickness constriction at the contactexit The selected pulse was analysed shyrstly using (53) to calculate the reregection

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 973

film

thic

knes

s (m

m)

1000

100

10

1

01

001

00010 10 20 30 40 50 60

f (MHz)

time of flight limit

resonance method limit

spring model upper limit (R = 09)

spring model lower limit (R = 01)

Figure 15 Limits of operation for macrlm-thickness measurement by ultrasonic means

coemacrcient and then using the spring model to predict the shylm thickness The speedof sound in the oil in the contact is set to c = 4400 m siexcl1 (determined using themethod described in x 3)

Figure 14 shows the measured shylm thickness plotted against a prediction of theshylm thickness from the solution for an elliptical contact of Dowson amp Higginson(1966) (equation (61)) The bearing and lubricant heats up during operation Thetemperature of the entrained oil was monitored and used to determine an appropriateviscosity with which to calculate the shylm thickness in (61) This was why the resultswere not plotted as shylm thickness against speed (as in shygure 11) because viscositywas varying throughout the test

The results in shygure 14 show good agreement between measured lubricant-shylmthickness and that predicted by the EHD regression equations The spread along thex-axis shows the variation in shylm for nominally the same bearing operating conditions(load speed and oil temperature) At this stage it is not clear whether this scatteris a result of the measurement process or whether this is the actual shylm thicknessin the bearing It is worth noting that this measurement process could be improvedif the exact position of the ball could be related to the ultrasonic measurement soallowing a more precise measurement of the minimum shylm thickness

7 Discussion limits of operation

It is instructive to consider the limits of shylm-thickness measurement for a given ultra-sonic frequency The simplest method for determining the thickness of a lubricantlayer providing it is sumacrciently thick is by measuring the ToF through the layerA reregection occurs at the layer front face and another at the back face The thick-ness is readily obtained from the time between the arrival of these pulses multipliedby the acoustic velocity For the method to work the two reregected pulses must besumacrciently discrete and so the propagation distance must be greater than the pulse

Proc R Soc Lond A (2003)

974 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

width and so the minimum shylm thickness detectable by this method is given by

h gtnc

2f (71)

where n is the number of wavelengths in the ultrasonic pulse typically around threeThis measurement limit is plotted in shygure 15 as the minimum frequency requiredto measure a given shylm thickness Conventional ultrasonic non-destructive testingis generally restricted by losses in the propagating media (steel in this case) tofrequencies below 4060 MHz From (71) this means that the ToF method is onlypractically useful for layers of thickness greater than 40 mm This is thicker than thatfound on most commercial bearing systems

A lubricant layer resonates at a frequency given by (23) This equation also givesthe low thickness limit for this technique as the upper frequency output by a giventransducer determined the lowest measurable layer thickness This limit is also shownin shygure 15 for the shyrst through-thickness mode (ie m = 1) So using the highestpractical frequencies shylms greater than 10 mm are measurable by the shylm-resonancemethod

The upper limit of shylm thickness measurable using the spring-model approach isreached as R tends to unity in (27) Experience shows that measurements of R lessthan 09 yield satisfactory results The lowest shylm thickness measurable will dependon the smallest possible value of R This in turn will depend on the signal-to-noiseratio A signal-to-noise ratio of 60 dB is typical for conventional ultrasonic non-destructive testing systems The noise amplitude is thus 1

1000of the pulse amplitude

In the case of a measurement on a real bearing the achievable signal-to-noise ratiowill be reduced by the transducer-bearing reregection coemacrcient and by the attenuationin the bearing shell This means that the pulse incident in the reguid shylm will bereduced from that output by the transducer by a factor of shyve (as a conservativeestimate) Further it is assumed that for reliable measurements a pulse reregectedfrom the oil layer should have an amplitude approximately 20 times that of the noiselevel This results in a minimum measurable reregection coemacrcient of R = 01 Therelationships between the shylm thickness and the transducer frequency for the upperlimit when R = 09 and the lower where R = 01 are shown in shygure 15

This indicates that for a measuring frequency of 60 MHz a lubricant shylm of 2 nmis measurable This opens up the possibility of measuring boundary-type lubricantshylms between machine elements However the models presented here are designedfor a parallel-sided oil layer completely separating the smooth bearing surface If atthese low shylm thickness metal-to-metal contact occurs then transmission will occurat this location In this case some alternative method for interpreting reregectioncoemacrcients will be needed

8 Conclusions

Ultrasound is reregected from the lubricant shylm between bearing surfaces It is possibleto deduce the thickness of the lubricant shylm by comparing the frequency spectrumof the reregected pulse with that of the incident pulse The response of the lubricantlayer to an ultrasonic pulse has been modelled using both a spring-model methodand a continuum method The spring model is suitable for thin lubricant shylms inwhich the wavelength of the ultrasound is much larger than the layer thickness The

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 975

continuum model is valid for all layer thicknesses and allows the prediction of thethrough-thickness resonant frequencies of the lubricant layers Measurement of thesethrough-thickness resonances also provides a means of measuring the layer thickness

Experiments on reguid layers between regat plates and eccentric rings have demon-strated that ultrasound can suitably measure a wide range of liquid layer thicknessThe EHD lubricant shylm that forms between a ball sliding on a regat surface hasalso been measured ultrasonically The measured results agree well with theoreti-cal predictions taking into account the greatly increased speed of sound throughthe lubricant when it is under high pressure Films in the range 50500 nm wererecorded

The approach can also be used to measure shylm thickness in a rolling-elementbearing An ultrasonic transducer was mounted on the bearing raceway and thepulse reregected from the lubricant layer generated as the ball passes was recordedAgain measured results agreed well with theoretical predictions

The lower limit of measurement by this method depends on the signal-to-noiseratio A continuum model showed that using frequencies up to 60 MHz permits themeasurement of 2 nm thick shylms There is no upper limit to shylm-thickness measure-ment Thick shylms (greater than 40 mm) can be measured by a time-of-regight methodFilms of intermediate thickness can be determined by measuring the frequency atwhich the shylm resonates

This work was funded by a grant from the UK Engineering and Physical Sciences ResearchCouncil under the ROPA programme The authors acknowledge the help of Phil Harper of theUniversity of Sheplusmneld for his assistance with some of the measurements

References

Astridge D G amp Longmacreld M D 1967 Capacitance measurement and oil macrlm thickness in alarge radius disc and ring machine Proc Inst Mech Engrs 182 8996

Cameron A amp Gohar R 1966 Theoretical and experimental studies of the oil macrlm in lubricatedpoint contact Proc R Soc Lond A 291 520536

Dowson D amp Higginson G R 1966 Elastohydrodynamic lubrication|the fundamentals of roller

and gear lubrication Oxford Pergamon

Drinkwater B W Dwyer-Joyce R S amp Cawley P 1996 A study of the interaction betweenultrasound and a partially contacting solidsolid interface Proc R Soc Lond A 452 26132628

El-Sisi S I amp Shawki G S A 1960 Measurement of oil-macrlm thickness between disks by electricalconductivity Trans ASME J Basic Engng 82 12

Hamilton G M amp Moore S L 1967 A modimacred gauge for investigating an elastohydrodynamiccontact Proc Inst Mech Engrs 182 251

Hamrock B J 1994 Fundamentals of deguid macrlm lubrication McGraw-Hill

Hosten B 1991 Bulk heterogeneous plane-wave propagation through viscoelastic plates andstratimacred media with large values of frequency-domain Ultrasonics 29 445450

Jacobson B O amp Vinet P 1987 A model for the indeguence of pressure on the bulk modulusand the indeguence of temperature on the solidimacrcation pressure for liquid lubricants Trans

ASME J Tribology 109 709

Johnston G J Wayte R amp Spikes H A 1991 The measurement and study of very thinlubricant macrlms in concentrated contacts Tribol Trans 34 187194

Kinra V K Jaminet P T Zhu C amp Iyer V R 1994 Simultaneous measurement of theacoustical properties of a thin-layered medium the inverse problem J Acoust Soc Am 9530593074

Proc R Soc Lond A (2003)

966 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

25

20

15

10

5

0

film

thic

knes

s (m

m)

60 65 70 75 80 85 90 95 100 105 110

f (MHz)

Figure 7 Film-thickness results determined by the application ofthe spring model to the redegection spectra of macrgure 6a

where Rl(f) is the reregection-coemacrcient spectrum of the lubricant layer which canthen be obtained by combining (51) and (52)

Rl(f) =Am eas (f)

Aref(f)Rgw (53)

Figure 6 shows two sets of reregection-coemacrcient spectra of liquid layers in a liquid-wedge experiment recorded using two dinoterent wide-band transducers for a rangeof shylm thickness The thickness of the liquid layer at any measuring location wasestimated from the geometry of the reguid wedge formed by the shim

From shygure 6b it can be seen that at higher shylm thicknesses resonant frequencies(observed as minima in the reregection-coemacrcient spectra) are visible When these res-onances occur the layer thickness can be readily determined from (23) For thinnerliquid layers andor when using lower-frequency transducers the resonance is notobserved as it occurs beyond the frequency range of the transducer However theshape of the reregection-coemacrcient spectrum below resonance can be used to predictthe thickness of the liquid layer though the application of the spring model (equa-tion (27))

The stinotness of the layer can be measured over a range of frequencies with onetransducer As the stinotness at a single frequency is sumacrcient to enable prediction ofthe reguid-layer thickness there is some redundancy in the data that can be used as amethod of checking the accuracy of the spring model Figure 7 shows the data given inshygure 6a converted to shylm thickness via (27) over the bandwidth of the transducerFrom shygure 7 it can be seen that for the lower shylm-thickness values the curvesare horizontal This indicates a good measurement as the shylm thickness cannot bea function of the frequency with which it is measured However for the top curvethe model does not correctly convert the reregection coemacrcient to a constant layerthickness This is because as the reregection coemacrcient tends to unity so the springmodel (equation (27)) becomes prone to numerical error For the next curve down

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 967

0

10

20

30

40

50

70

mea

sure

d f

ilm

thic

kness

(m

m)

60

predicted film thickness (mm)

10 20 30 40 50 60 70

Figure 8 Film-thickness values measured by ultrasonic redegection compared withpredictions of the thickness determined from the geometry of the deguid wedge

at the higher frequencies the same happens This represents a limit of the spring-model approach and to measure these thicker shylms either lower frequencies shouldbe used so R is lower or higher frequencies used and the location of resonancesdetermined

Figure 8 shows ultrasonic measurements of the thickness of the liquid shylm com-pared with the geometrical prediction of the layer thickness The data below 25 mmcorrespond to measurements performed using the spring model while the data above25 mm have been determined from the measurement of shylm resonances Agreementis good (and a straight line is observed) but in practice the measured liquid-layerthickness tends to be slightly larger than that of the shim This is likely to becaused by either some thin residual of water between the shim of the glass plateor by deformation of the shim where it has been cut Each of these enotects wouldtend to make the liquid layer thicker and hence explain the dinoterence seen in shyg-ure 8

(b) Annular oil-macrlm apparatus

Figure 9 shows the apparatus to create an oil wedge between a ring and a shaft Thering and shaft were made from aluminium The ringshaft interface had a nominaldiameter of 70 mm and a diametral clearance of 100 mm The shaft was spring loadedagainst the ring By changing the position of the loading point the gap thicknessin the region above the transducer could be varied The gap was shylled with mineraloil (Shell Turbo T68) through a small shyller hole A 25 MHz focused transducer waslocated in a water bath beneath the assembly The transducer was positioned so thatthe wave was focused on the reguid layer

Figure 10 shows a plot of the shylm thickness determined from the reregection mea-surements for various angular positions of the loading point relative to the ultra-sonic measurement position In this case all the shylms were measured using theshylm-resonance method The theoretical width of annular gap h between eccentriccylinders is obtained from geometry

h = R1

middot

1 iexcl

micro

R1 iexcl R2

R1

para2

sin2 iquest

cedil1=2

iexcl R2 + (R1 iexcl R2) cos iquest (54)

Proc R Soc Lond A (2003)

968 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

transducer

water tank

measurement zone

oil-filled annulus

tension spring

aluminium cylinders

Figure 9 Apparatus used to create an annular oil macrlm for ultrasonic-redegection experiments

film

thic

knes

s (m

m)

100

90

80

70

60

50

40

30

20

10

0

angular position (deg)

-180 -135 -90 -45 0 45 90 135 180

ultrasonic measurements

mathematical solution

Figure 10 Film-thickness values measured by ultrasonic redegection for an annular macrlm betweentwo eccentric cylinders Experimental results are compared with the geometrical solution

where R1 and R2 are the radii of the bush and shaft respectively and rsquo is theangle measured from the point of contact Equation (54) is included in shygure 10 forcomparison and a good correlation was observed

To reduce the enotects of the curvature of the lubricated interface the transducersused in this experiment focus the wave onto the oil layer The spot size of the focusedwave varies with frequency according to the relationship (Silk 1984)

df(iexcl6 d B) =1028F c

fD (55)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 969

steel disc water bath

oil meniscus

rotating steel ball

transducer

hydraulic load

motor drive

Figure 11 Schematic of the experimental apparatus used to generatean EHD macrlm for a ball sliding on a degat

where df is the diameter of the spot size (where the signal has reduced to iexcl6 dBof its peak value) F is the transducer focusing length f is the wave frequencyc is the speed of sound in water and D is the diameter of the piezoelectric elementFor a 25 MHz frequency wave this corresponds to a spot size in water of 522 mmThis is small compared with the radius of the shaftbush apparatus So essentiallythe transducer is receiving signals back from a regat region of constant shylm thick-ness and the curvature has little enotect The good agreement between experimen-tal and theoretical liquid-layer thickness shown in shygure 10 further validates thishypothesis

6 Measurement of dynamic lubricating macrlms

An EHD lubricant shylm forms between rolling or sliding non-conformal contactsTypically the thickness of the oil layer is in the region of 011 mm This is withinthe range of the possible measurement by ultrasonic means and within the spring-model regime of ultrasonic response In this work EHD shylms have been measuredin a model rig containing a single stationary lubricated contact and in a rolling-element bearing where the lubricant shylm is transient (with respect to the trans-ducer)

(a) Ball on disc EHD lubrication apparatus

Figure 11 shows the apparatus used to generate a single EHD lubricated contactA steel ball is supported on rollers and hydraulically loaded onto the underside ofa steel disc The ball is rotated at constant speed by an electric motor througha gear box and quill shaft The steel disc is held stationary such that the ball iscompletely sliding against the underside of the disc This apparatus is a modishyed`optical elastohydrodynamicrsquo apparatus (originally developed by Cameron amp Gohar(1966)) where the semi-reregective rotating glass disc has been replaced by a station-

Proc R Soc Lond A (2003)

970 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

005

010

015

020

025

030

035

040

0 02 04 06 08 10 12 14

lubri

can

t fi

lm thic

kness

(m

m)

entrainment speed (m s-1)

theoretical solution a = 015 mmmeasurements a = 015 mmtheoretical solution a = 01 mmmeasurements a = 01 mm

Figure 12 EHD lubricant-macrlm-thickness variation with ball-sliding speed for two loadsUltrasonic-redegection measurements are compared with a theoretical solution

ary steel disc and the microscope replaced by an ultrasonic transducer The balldisc contact was regooded with a mineral oil (Shell Turbo T68) which is entrainedinto the contact to form an EHD shylm A 50 MHz focused transducer was mountedabove the contact in a water bath The transducer was positioned directly abovethe contact region and at a distance such that the wave is focused on the balldiscinterface

Reregected pulses were recorded from the discball interface as the ball rotationalspeed and load were varied A reference spectrum was obtained by recording the pulsereregected when the ball was out of contact with the disc but the disc was still regoodedwith oil As in the wedge experiment the reference and lubricant-layer measurementswere used in (32) to obtain the reregection-coemacrcient spectrum of the lubricant layerA series of reregection coemacrcient spectra were then recorded from the discball contactas the sliding speed was increased The spring model (equation (27)) was used todetermine the shylm thickness from these spectra An automated LabView interfacewas written to record the spectra divide by a reference and convert the data intoshylm thickness (as shown in shygure 6) As discussed in x 3 above the density and speedof sound of the oil used in (27) are those at contact pressure (in this case 08 GPa)and not those in the bulk

Figure 12 shows the measured variation in shylm thickness determined from thereregection coemacrcient spectra as the speed is increased for two load cases (giving con-tact radii a of 01 and 015 mm) For this lubrication case a theoretical predictionof the oil-shylm thickness can be obtained from the regression equations of Dowson ampHigginson (1966) The central shylm thickness hc is expressed as a regression equationconsisting of shyve non-dimensional parameters

Hc = 269U 067G053W iexcl0067(1 iexcl 061eiexcl073k) (61)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 971

test rolling bearing

measurement zone

hydraulic loading

focusing transducer

water bath

belt and pulley drive

Figure 13 Schematic of apparatus used for ultrasonic measurementsof macrlm thickness in rolling-element bearings

where

Hc =hc

Rx

W =P

2EcurrenR2x

U =sup20u

2EcurrenRx

k = 103

micro

Ry

Rx

para064

G = 2notEcurren

where Ecurren is the reduced modulus Rx and Ry are the reduced radii in the paralleland transverse directions u is the mean surface speed P is the applied contact loadsup20 is the viscosity of oil in the inlet and not is its pressure-viscosity coemacrcient

The predictions of (61) for the two load cases are plotted in shygure 12 The agree-ment between the theoretical solution and the experimental data is good Typicallythe measured data are repeatable to within sect20 The oil shylm generated by theapparatus is not completely stable To directly observe the lubricant shylm the steeldisc was replaced by the glass disc and the shylm monitored visually A certain amountof shylm reguctuation was observed during normal running (caused by a slight processingof the ball on its supporting rollers) Notwithstanding the results are encouragingbecause this indicates that both the integrity of the ultrasonic method and alsothat the speed of sound of the lubricating oil compares well with predictions fromhigh-pressure measurements

(b) Rolling bearing lubricant-macrlm measurement

The duration of the ultrasonic pulses used in this work was short Spatially thepulse width was typically three wavelengths in length A 25 MHz wave travelling insteel results in a pulse duration of 01 ms Therefore it is feasible to record the shylmthickness in a rolling element moving past the focal point of an ultrasonic transducer

The approach has been used to measure shylm thickness in a 6410 deep-grooveball bearing Figure 13 shows a schematic of the bearing and the positioning of thetransducer The 25 MHz transducer (see table 2 for details) was located in a small

Proc R Soc Lond A (2003)

972 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

0

01

02

03

04

05

07

01 02 03 04 05 06 07

theo

reti

cal

film

thic

knes

s pre

dic

tion (

mm

)

45 kN 112 RPM 60 kN 72 RPM

60 kN 103 RPM 60 kN 128 RPM

60 kN 135 RPM 60 kN 137 RPM

60 kN 178 RPM 60 kN 195 RPM

60 kN 297 RPM 60 kN 375 RPM

75 kN 48 RPM 75 kN 124 RPM

06

measured film thickness (mm)

Figure 14 Comparison of rolling-element-bearing macrlm thickness measured byan ultrasonic means with EHD theoretical solution

water bath machined out of the bearing bush The transducer was spherically focusedand positioned in the water bath so that the wave was focused on the contact betweena ball and the raceway The bearing was loaded hydraulically and rotated by anelectric motor The bearing cavity was regooded with a mineral oil (Shell Turbo T68) Athermocouple was positioned on the outer raceway near the ultrasonic measurementpoint The bearing was loaded to give a contact eclipse between the ball and theouter raceway of semi-major and semi-minor axes 115 and 08 mm respectivelyThe bearing was then rotated and the transducer set to continuously pulse at arepetition rate of 10 kHz

The focal spot size of the transducer was ca 500 mm The maximum rotationalspeed of the bearing in these tests was 375 rpm At this rotational speed theregion of focused ultrasound would remain completely within the lubricated con-tact for ca 05 ms This allowed approximately shyve discrete pulses of ultrasound tobe reregected from the lubricant shylm as each ball passed through the measurementzone Initially a reference reregected pulse was recorded when the bearing was station-ary and there was no ball located over the measurement zone (although the cavitywas still shylled with oil) If a pulse is incident on an EHD shylm its amplitude is reducedbecause part of the wave has been transmitted through the oil shylm into the ball Bycontinuously monitoring the signals reregected from the raceway measurements of theball-raceway contacts were made Of the shyve pulses reregected from the ball-racewaycontact the lowest amplitude pulse was selected for analysis This pulse correspondsto the thinnest measured shylm thickness It should be noted that the resolution of thefocused transducer and the measurement interval are such that it was not possibleto record the horseshoe-shaped minimum shylm-thickness constriction at the contactexit The selected pulse was analysed shyrstly using (53) to calculate the reregection

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 973

film

thic

knes

s (m

m)

1000

100

10

1

01

001

00010 10 20 30 40 50 60

f (MHz)

time of flight limit

resonance method limit

spring model upper limit (R = 09)

spring model lower limit (R = 01)

Figure 15 Limits of operation for macrlm-thickness measurement by ultrasonic means

coemacrcient and then using the spring model to predict the shylm thickness The speedof sound in the oil in the contact is set to c = 4400 m siexcl1 (determined using themethod described in x 3)

Figure 14 shows the measured shylm thickness plotted against a prediction of theshylm thickness from the solution for an elliptical contact of Dowson amp Higginson(1966) (equation (61)) The bearing and lubricant heats up during operation Thetemperature of the entrained oil was monitored and used to determine an appropriateviscosity with which to calculate the shylm thickness in (61) This was why the resultswere not plotted as shylm thickness against speed (as in shygure 11) because viscositywas varying throughout the test

The results in shygure 14 show good agreement between measured lubricant-shylmthickness and that predicted by the EHD regression equations The spread along thex-axis shows the variation in shylm for nominally the same bearing operating conditions(load speed and oil temperature) At this stage it is not clear whether this scatteris a result of the measurement process or whether this is the actual shylm thicknessin the bearing It is worth noting that this measurement process could be improvedif the exact position of the ball could be related to the ultrasonic measurement soallowing a more precise measurement of the minimum shylm thickness

7 Discussion limits of operation

It is instructive to consider the limits of shylm-thickness measurement for a given ultra-sonic frequency The simplest method for determining the thickness of a lubricantlayer providing it is sumacrciently thick is by measuring the ToF through the layerA reregection occurs at the layer front face and another at the back face The thick-ness is readily obtained from the time between the arrival of these pulses multipliedby the acoustic velocity For the method to work the two reregected pulses must besumacrciently discrete and so the propagation distance must be greater than the pulse

Proc R Soc Lond A (2003)

974 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

width and so the minimum shylm thickness detectable by this method is given by

h gtnc

2f (71)

where n is the number of wavelengths in the ultrasonic pulse typically around threeThis measurement limit is plotted in shygure 15 as the minimum frequency requiredto measure a given shylm thickness Conventional ultrasonic non-destructive testingis generally restricted by losses in the propagating media (steel in this case) tofrequencies below 4060 MHz From (71) this means that the ToF method is onlypractically useful for layers of thickness greater than 40 mm This is thicker than thatfound on most commercial bearing systems

A lubricant layer resonates at a frequency given by (23) This equation also givesthe low thickness limit for this technique as the upper frequency output by a giventransducer determined the lowest measurable layer thickness This limit is also shownin shygure 15 for the shyrst through-thickness mode (ie m = 1) So using the highestpractical frequencies shylms greater than 10 mm are measurable by the shylm-resonancemethod

The upper limit of shylm thickness measurable using the spring-model approach isreached as R tends to unity in (27) Experience shows that measurements of R lessthan 09 yield satisfactory results The lowest shylm thickness measurable will dependon the smallest possible value of R This in turn will depend on the signal-to-noiseratio A signal-to-noise ratio of 60 dB is typical for conventional ultrasonic non-destructive testing systems The noise amplitude is thus 1

1000of the pulse amplitude

In the case of a measurement on a real bearing the achievable signal-to-noise ratiowill be reduced by the transducer-bearing reregection coemacrcient and by the attenuationin the bearing shell This means that the pulse incident in the reguid shylm will bereduced from that output by the transducer by a factor of shyve (as a conservativeestimate) Further it is assumed that for reliable measurements a pulse reregectedfrom the oil layer should have an amplitude approximately 20 times that of the noiselevel This results in a minimum measurable reregection coemacrcient of R = 01 Therelationships between the shylm thickness and the transducer frequency for the upperlimit when R = 09 and the lower where R = 01 are shown in shygure 15

This indicates that for a measuring frequency of 60 MHz a lubricant shylm of 2 nmis measurable This opens up the possibility of measuring boundary-type lubricantshylms between machine elements However the models presented here are designedfor a parallel-sided oil layer completely separating the smooth bearing surface If atthese low shylm thickness metal-to-metal contact occurs then transmission will occurat this location In this case some alternative method for interpreting reregectioncoemacrcients will be needed

8 Conclusions

Ultrasound is reregected from the lubricant shylm between bearing surfaces It is possibleto deduce the thickness of the lubricant shylm by comparing the frequency spectrumof the reregected pulse with that of the incident pulse The response of the lubricantlayer to an ultrasonic pulse has been modelled using both a spring-model methodand a continuum method The spring model is suitable for thin lubricant shylms inwhich the wavelength of the ultrasound is much larger than the layer thickness The

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 975

continuum model is valid for all layer thicknesses and allows the prediction of thethrough-thickness resonant frequencies of the lubricant layers Measurement of thesethrough-thickness resonances also provides a means of measuring the layer thickness

Experiments on reguid layers between regat plates and eccentric rings have demon-strated that ultrasound can suitably measure a wide range of liquid layer thicknessThe EHD lubricant shylm that forms between a ball sliding on a regat surface hasalso been measured ultrasonically The measured results agree well with theoreti-cal predictions taking into account the greatly increased speed of sound throughthe lubricant when it is under high pressure Films in the range 50500 nm wererecorded

The approach can also be used to measure shylm thickness in a rolling-elementbearing An ultrasonic transducer was mounted on the bearing raceway and thepulse reregected from the lubricant layer generated as the ball passes was recordedAgain measured results agreed well with theoretical predictions

The lower limit of measurement by this method depends on the signal-to-noiseratio A continuum model showed that using frequencies up to 60 MHz permits themeasurement of 2 nm thick shylms There is no upper limit to shylm-thickness measure-ment Thick shylms (greater than 40 mm) can be measured by a time-of-regight methodFilms of intermediate thickness can be determined by measuring the frequency atwhich the shylm resonates

This work was funded by a grant from the UK Engineering and Physical Sciences ResearchCouncil under the ROPA programme The authors acknowledge the help of Phil Harper of theUniversity of Sheplusmneld for his assistance with some of the measurements

References

Astridge D G amp Longmacreld M D 1967 Capacitance measurement and oil macrlm thickness in alarge radius disc and ring machine Proc Inst Mech Engrs 182 8996

Cameron A amp Gohar R 1966 Theoretical and experimental studies of the oil macrlm in lubricatedpoint contact Proc R Soc Lond A 291 520536

Dowson D amp Higginson G R 1966 Elastohydrodynamic lubrication|the fundamentals of roller

and gear lubrication Oxford Pergamon

Drinkwater B W Dwyer-Joyce R S amp Cawley P 1996 A study of the interaction betweenultrasound and a partially contacting solidsolid interface Proc R Soc Lond A 452 26132628

El-Sisi S I amp Shawki G S A 1960 Measurement of oil-macrlm thickness between disks by electricalconductivity Trans ASME J Basic Engng 82 12

Hamilton G M amp Moore S L 1967 A modimacred gauge for investigating an elastohydrodynamiccontact Proc Inst Mech Engrs 182 251

Hamrock B J 1994 Fundamentals of deguid macrlm lubrication McGraw-Hill

Hosten B 1991 Bulk heterogeneous plane-wave propagation through viscoelastic plates andstratimacred media with large values of frequency-domain Ultrasonics 29 445450

Jacobson B O amp Vinet P 1987 A model for the indeguence of pressure on the bulk modulusand the indeguence of temperature on the solidimacrcation pressure for liquid lubricants Trans

ASME J Tribology 109 709

Johnston G J Wayte R amp Spikes H A 1991 The measurement and study of very thinlubricant macrlms in concentrated contacts Tribol Trans 34 187194

Kinra V K Jaminet P T Zhu C amp Iyer V R 1994 Simultaneous measurement of theacoustical properties of a thin-layered medium the inverse problem J Acoust Soc Am 9530593074

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 967

0

10

20

30

40

50

70

mea

sure

d f

ilm

thic

kness

(m

m)

60

predicted film thickness (mm)

10 20 30 40 50 60 70

Figure 8 Film-thickness values measured by ultrasonic redegection compared withpredictions of the thickness determined from the geometry of the deguid wedge

at the higher frequencies the same happens This represents a limit of the spring-model approach and to measure these thicker shylms either lower frequencies shouldbe used so R is lower or higher frequencies used and the location of resonancesdetermined

Figure 8 shows ultrasonic measurements of the thickness of the liquid shylm com-pared with the geometrical prediction of the layer thickness The data below 25 mmcorrespond to measurements performed using the spring model while the data above25 mm have been determined from the measurement of shylm resonances Agreementis good (and a straight line is observed) but in practice the measured liquid-layerthickness tends to be slightly larger than that of the shim This is likely to becaused by either some thin residual of water between the shim of the glass plateor by deformation of the shim where it has been cut Each of these enotects wouldtend to make the liquid layer thicker and hence explain the dinoterence seen in shyg-ure 8

(b) Annular oil-macrlm apparatus

Figure 9 shows the apparatus to create an oil wedge between a ring and a shaft Thering and shaft were made from aluminium The ringshaft interface had a nominaldiameter of 70 mm and a diametral clearance of 100 mm The shaft was spring loadedagainst the ring By changing the position of the loading point the gap thicknessin the region above the transducer could be varied The gap was shylled with mineraloil (Shell Turbo T68) through a small shyller hole A 25 MHz focused transducer waslocated in a water bath beneath the assembly The transducer was positioned so thatthe wave was focused on the reguid layer

Figure 10 shows a plot of the shylm thickness determined from the reregection mea-surements for various angular positions of the loading point relative to the ultra-sonic measurement position In this case all the shylms were measured using theshylm-resonance method The theoretical width of annular gap h between eccentriccylinders is obtained from geometry

h = R1

middot

1 iexcl

micro

R1 iexcl R2

R1

para2

sin2 iquest

cedil1=2

iexcl R2 + (R1 iexcl R2) cos iquest (54)

Proc R Soc Lond A (2003)

968 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

transducer

water tank

measurement zone

oil-filled annulus

tension spring

aluminium cylinders

Figure 9 Apparatus used to create an annular oil macrlm for ultrasonic-redegection experiments

film

thic

knes

s (m

m)

100

90

80

70

60

50

40

30

20

10

0

angular position (deg)

-180 -135 -90 -45 0 45 90 135 180

ultrasonic measurements

mathematical solution

Figure 10 Film-thickness values measured by ultrasonic redegection for an annular macrlm betweentwo eccentric cylinders Experimental results are compared with the geometrical solution

where R1 and R2 are the radii of the bush and shaft respectively and rsquo is theangle measured from the point of contact Equation (54) is included in shygure 10 forcomparison and a good correlation was observed

To reduce the enotects of the curvature of the lubricated interface the transducersused in this experiment focus the wave onto the oil layer The spot size of the focusedwave varies with frequency according to the relationship (Silk 1984)

df(iexcl6 d B) =1028F c

fD (55)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 969

steel disc water bath

oil meniscus

rotating steel ball

transducer

hydraulic load

motor drive

Figure 11 Schematic of the experimental apparatus used to generatean EHD macrlm for a ball sliding on a degat

where df is the diameter of the spot size (where the signal has reduced to iexcl6 dBof its peak value) F is the transducer focusing length f is the wave frequencyc is the speed of sound in water and D is the diameter of the piezoelectric elementFor a 25 MHz frequency wave this corresponds to a spot size in water of 522 mmThis is small compared with the radius of the shaftbush apparatus So essentiallythe transducer is receiving signals back from a regat region of constant shylm thick-ness and the curvature has little enotect The good agreement between experimen-tal and theoretical liquid-layer thickness shown in shygure 10 further validates thishypothesis

6 Measurement of dynamic lubricating macrlms

An EHD lubricant shylm forms between rolling or sliding non-conformal contactsTypically the thickness of the oil layer is in the region of 011 mm This is withinthe range of the possible measurement by ultrasonic means and within the spring-model regime of ultrasonic response In this work EHD shylms have been measuredin a model rig containing a single stationary lubricated contact and in a rolling-element bearing where the lubricant shylm is transient (with respect to the trans-ducer)

(a) Ball on disc EHD lubrication apparatus

Figure 11 shows the apparatus used to generate a single EHD lubricated contactA steel ball is supported on rollers and hydraulically loaded onto the underside ofa steel disc The ball is rotated at constant speed by an electric motor througha gear box and quill shaft The steel disc is held stationary such that the ball iscompletely sliding against the underside of the disc This apparatus is a modishyed`optical elastohydrodynamicrsquo apparatus (originally developed by Cameron amp Gohar(1966)) where the semi-reregective rotating glass disc has been replaced by a station-

Proc R Soc Lond A (2003)

970 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

005

010

015

020

025

030

035

040

0 02 04 06 08 10 12 14

lubri

can

t fi

lm thic

kness

(m

m)

entrainment speed (m s-1)

theoretical solution a = 015 mmmeasurements a = 015 mmtheoretical solution a = 01 mmmeasurements a = 01 mm

Figure 12 EHD lubricant-macrlm-thickness variation with ball-sliding speed for two loadsUltrasonic-redegection measurements are compared with a theoretical solution

ary steel disc and the microscope replaced by an ultrasonic transducer The balldisc contact was regooded with a mineral oil (Shell Turbo T68) which is entrainedinto the contact to form an EHD shylm A 50 MHz focused transducer was mountedabove the contact in a water bath The transducer was positioned directly abovethe contact region and at a distance such that the wave is focused on the balldiscinterface

Reregected pulses were recorded from the discball interface as the ball rotationalspeed and load were varied A reference spectrum was obtained by recording the pulsereregected when the ball was out of contact with the disc but the disc was still regoodedwith oil As in the wedge experiment the reference and lubricant-layer measurementswere used in (32) to obtain the reregection-coemacrcient spectrum of the lubricant layerA series of reregection coemacrcient spectra were then recorded from the discball contactas the sliding speed was increased The spring model (equation (27)) was used todetermine the shylm thickness from these spectra An automated LabView interfacewas written to record the spectra divide by a reference and convert the data intoshylm thickness (as shown in shygure 6) As discussed in x 3 above the density and speedof sound of the oil used in (27) are those at contact pressure (in this case 08 GPa)and not those in the bulk

Figure 12 shows the measured variation in shylm thickness determined from thereregection coemacrcient spectra as the speed is increased for two load cases (giving con-tact radii a of 01 and 015 mm) For this lubrication case a theoretical predictionof the oil-shylm thickness can be obtained from the regression equations of Dowson ampHigginson (1966) The central shylm thickness hc is expressed as a regression equationconsisting of shyve non-dimensional parameters

Hc = 269U 067G053W iexcl0067(1 iexcl 061eiexcl073k) (61)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 971

test rolling bearing

measurement zone

hydraulic loading

focusing transducer

water bath

belt and pulley drive

Figure 13 Schematic of apparatus used for ultrasonic measurementsof macrlm thickness in rolling-element bearings

where

Hc =hc

Rx

W =P

2EcurrenR2x

U =sup20u

2EcurrenRx

k = 103

micro

Ry

Rx

para064

G = 2notEcurren

where Ecurren is the reduced modulus Rx and Ry are the reduced radii in the paralleland transverse directions u is the mean surface speed P is the applied contact loadsup20 is the viscosity of oil in the inlet and not is its pressure-viscosity coemacrcient

The predictions of (61) for the two load cases are plotted in shygure 12 The agree-ment between the theoretical solution and the experimental data is good Typicallythe measured data are repeatable to within sect20 The oil shylm generated by theapparatus is not completely stable To directly observe the lubricant shylm the steeldisc was replaced by the glass disc and the shylm monitored visually A certain amountof shylm reguctuation was observed during normal running (caused by a slight processingof the ball on its supporting rollers) Notwithstanding the results are encouragingbecause this indicates that both the integrity of the ultrasonic method and alsothat the speed of sound of the lubricating oil compares well with predictions fromhigh-pressure measurements

(b) Rolling bearing lubricant-macrlm measurement

The duration of the ultrasonic pulses used in this work was short Spatially thepulse width was typically three wavelengths in length A 25 MHz wave travelling insteel results in a pulse duration of 01 ms Therefore it is feasible to record the shylmthickness in a rolling element moving past the focal point of an ultrasonic transducer

The approach has been used to measure shylm thickness in a 6410 deep-grooveball bearing Figure 13 shows a schematic of the bearing and the positioning of thetransducer The 25 MHz transducer (see table 2 for details) was located in a small

Proc R Soc Lond A (2003)

972 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

0

01

02

03

04

05

07

01 02 03 04 05 06 07

theo

reti

cal

film

thic

knes

s pre

dic

tion (

mm

)

45 kN 112 RPM 60 kN 72 RPM

60 kN 103 RPM 60 kN 128 RPM

60 kN 135 RPM 60 kN 137 RPM

60 kN 178 RPM 60 kN 195 RPM

60 kN 297 RPM 60 kN 375 RPM

75 kN 48 RPM 75 kN 124 RPM

06

measured film thickness (mm)

Figure 14 Comparison of rolling-element-bearing macrlm thickness measured byan ultrasonic means with EHD theoretical solution

water bath machined out of the bearing bush The transducer was spherically focusedand positioned in the water bath so that the wave was focused on the contact betweena ball and the raceway The bearing was loaded hydraulically and rotated by anelectric motor The bearing cavity was regooded with a mineral oil (Shell Turbo T68) Athermocouple was positioned on the outer raceway near the ultrasonic measurementpoint The bearing was loaded to give a contact eclipse between the ball and theouter raceway of semi-major and semi-minor axes 115 and 08 mm respectivelyThe bearing was then rotated and the transducer set to continuously pulse at arepetition rate of 10 kHz

The focal spot size of the transducer was ca 500 mm The maximum rotationalspeed of the bearing in these tests was 375 rpm At this rotational speed theregion of focused ultrasound would remain completely within the lubricated con-tact for ca 05 ms This allowed approximately shyve discrete pulses of ultrasound tobe reregected from the lubricant shylm as each ball passed through the measurementzone Initially a reference reregected pulse was recorded when the bearing was station-ary and there was no ball located over the measurement zone (although the cavitywas still shylled with oil) If a pulse is incident on an EHD shylm its amplitude is reducedbecause part of the wave has been transmitted through the oil shylm into the ball Bycontinuously monitoring the signals reregected from the raceway measurements of theball-raceway contacts were made Of the shyve pulses reregected from the ball-racewaycontact the lowest amplitude pulse was selected for analysis This pulse correspondsto the thinnest measured shylm thickness It should be noted that the resolution of thefocused transducer and the measurement interval are such that it was not possibleto record the horseshoe-shaped minimum shylm-thickness constriction at the contactexit The selected pulse was analysed shyrstly using (53) to calculate the reregection

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 973

film

thic

knes

s (m

m)

1000

100

10

1

01

001

00010 10 20 30 40 50 60

f (MHz)

time of flight limit

resonance method limit

spring model upper limit (R = 09)

spring model lower limit (R = 01)

Figure 15 Limits of operation for macrlm-thickness measurement by ultrasonic means

coemacrcient and then using the spring model to predict the shylm thickness The speedof sound in the oil in the contact is set to c = 4400 m siexcl1 (determined using themethod described in x 3)

Figure 14 shows the measured shylm thickness plotted against a prediction of theshylm thickness from the solution for an elliptical contact of Dowson amp Higginson(1966) (equation (61)) The bearing and lubricant heats up during operation Thetemperature of the entrained oil was monitored and used to determine an appropriateviscosity with which to calculate the shylm thickness in (61) This was why the resultswere not plotted as shylm thickness against speed (as in shygure 11) because viscositywas varying throughout the test

The results in shygure 14 show good agreement between measured lubricant-shylmthickness and that predicted by the EHD regression equations The spread along thex-axis shows the variation in shylm for nominally the same bearing operating conditions(load speed and oil temperature) At this stage it is not clear whether this scatteris a result of the measurement process or whether this is the actual shylm thicknessin the bearing It is worth noting that this measurement process could be improvedif the exact position of the ball could be related to the ultrasonic measurement soallowing a more precise measurement of the minimum shylm thickness

7 Discussion limits of operation

It is instructive to consider the limits of shylm-thickness measurement for a given ultra-sonic frequency The simplest method for determining the thickness of a lubricantlayer providing it is sumacrciently thick is by measuring the ToF through the layerA reregection occurs at the layer front face and another at the back face The thick-ness is readily obtained from the time between the arrival of these pulses multipliedby the acoustic velocity For the method to work the two reregected pulses must besumacrciently discrete and so the propagation distance must be greater than the pulse

Proc R Soc Lond A (2003)

974 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

width and so the minimum shylm thickness detectable by this method is given by

h gtnc

2f (71)

where n is the number of wavelengths in the ultrasonic pulse typically around threeThis measurement limit is plotted in shygure 15 as the minimum frequency requiredto measure a given shylm thickness Conventional ultrasonic non-destructive testingis generally restricted by losses in the propagating media (steel in this case) tofrequencies below 4060 MHz From (71) this means that the ToF method is onlypractically useful for layers of thickness greater than 40 mm This is thicker than thatfound on most commercial bearing systems

A lubricant layer resonates at a frequency given by (23) This equation also givesthe low thickness limit for this technique as the upper frequency output by a giventransducer determined the lowest measurable layer thickness This limit is also shownin shygure 15 for the shyrst through-thickness mode (ie m = 1) So using the highestpractical frequencies shylms greater than 10 mm are measurable by the shylm-resonancemethod

The upper limit of shylm thickness measurable using the spring-model approach isreached as R tends to unity in (27) Experience shows that measurements of R lessthan 09 yield satisfactory results The lowest shylm thickness measurable will dependon the smallest possible value of R This in turn will depend on the signal-to-noiseratio A signal-to-noise ratio of 60 dB is typical for conventional ultrasonic non-destructive testing systems The noise amplitude is thus 1

1000of the pulse amplitude

In the case of a measurement on a real bearing the achievable signal-to-noise ratiowill be reduced by the transducer-bearing reregection coemacrcient and by the attenuationin the bearing shell This means that the pulse incident in the reguid shylm will bereduced from that output by the transducer by a factor of shyve (as a conservativeestimate) Further it is assumed that for reliable measurements a pulse reregectedfrom the oil layer should have an amplitude approximately 20 times that of the noiselevel This results in a minimum measurable reregection coemacrcient of R = 01 Therelationships between the shylm thickness and the transducer frequency for the upperlimit when R = 09 and the lower where R = 01 are shown in shygure 15

This indicates that for a measuring frequency of 60 MHz a lubricant shylm of 2 nmis measurable This opens up the possibility of measuring boundary-type lubricantshylms between machine elements However the models presented here are designedfor a parallel-sided oil layer completely separating the smooth bearing surface If atthese low shylm thickness metal-to-metal contact occurs then transmission will occurat this location In this case some alternative method for interpreting reregectioncoemacrcients will be needed

8 Conclusions

Ultrasound is reregected from the lubricant shylm between bearing surfaces It is possibleto deduce the thickness of the lubricant shylm by comparing the frequency spectrumof the reregected pulse with that of the incident pulse The response of the lubricantlayer to an ultrasonic pulse has been modelled using both a spring-model methodand a continuum method The spring model is suitable for thin lubricant shylms inwhich the wavelength of the ultrasound is much larger than the layer thickness The

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 975

continuum model is valid for all layer thicknesses and allows the prediction of thethrough-thickness resonant frequencies of the lubricant layers Measurement of thesethrough-thickness resonances also provides a means of measuring the layer thickness

Experiments on reguid layers between regat plates and eccentric rings have demon-strated that ultrasound can suitably measure a wide range of liquid layer thicknessThe EHD lubricant shylm that forms between a ball sliding on a regat surface hasalso been measured ultrasonically The measured results agree well with theoreti-cal predictions taking into account the greatly increased speed of sound throughthe lubricant when it is under high pressure Films in the range 50500 nm wererecorded

The approach can also be used to measure shylm thickness in a rolling-elementbearing An ultrasonic transducer was mounted on the bearing raceway and thepulse reregected from the lubricant layer generated as the ball passes was recordedAgain measured results agreed well with theoretical predictions

The lower limit of measurement by this method depends on the signal-to-noiseratio A continuum model showed that using frequencies up to 60 MHz permits themeasurement of 2 nm thick shylms There is no upper limit to shylm-thickness measure-ment Thick shylms (greater than 40 mm) can be measured by a time-of-regight methodFilms of intermediate thickness can be determined by measuring the frequency atwhich the shylm resonates

This work was funded by a grant from the UK Engineering and Physical Sciences ResearchCouncil under the ROPA programme The authors acknowledge the help of Phil Harper of theUniversity of Sheplusmneld for his assistance with some of the measurements

References

Astridge D G amp Longmacreld M D 1967 Capacitance measurement and oil macrlm thickness in alarge radius disc and ring machine Proc Inst Mech Engrs 182 8996

Cameron A amp Gohar R 1966 Theoretical and experimental studies of the oil macrlm in lubricatedpoint contact Proc R Soc Lond A 291 520536

Dowson D amp Higginson G R 1966 Elastohydrodynamic lubrication|the fundamentals of roller

and gear lubrication Oxford Pergamon

Drinkwater B W Dwyer-Joyce R S amp Cawley P 1996 A study of the interaction betweenultrasound and a partially contacting solidsolid interface Proc R Soc Lond A 452 26132628

El-Sisi S I amp Shawki G S A 1960 Measurement of oil-macrlm thickness between disks by electricalconductivity Trans ASME J Basic Engng 82 12

Hamilton G M amp Moore S L 1967 A modimacred gauge for investigating an elastohydrodynamiccontact Proc Inst Mech Engrs 182 251

Hamrock B J 1994 Fundamentals of deguid macrlm lubrication McGraw-Hill

Hosten B 1991 Bulk heterogeneous plane-wave propagation through viscoelastic plates andstratimacred media with large values of frequency-domain Ultrasonics 29 445450

Jacobson B O amp Vinet P 1987 A model for the indeguence of pressure on the bulk modulusand the indeguence of temperature on the solidimacrcation pressure for liquid lubricants Trans

ASME J Tribology 109 709

Johnston G J Wayte R amp Spikes H A 1991 The measurement and study of very thinlubricant macrlms in concentrated contacts Tribol Trans 34 187194

Kinra V K Jaminet P T Zhu C amp Iyer V R 1994 Simultaneous measurement of theacoustical properties of a thin-layered medium the inverse problem J Acoust Soc Am 9530593074

Proc R Soc Lond A (2003)

968 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

transducer

water tank

measurement zone

oil-filled annulus

tension spring

aluminium cylinders

Figure 9 Apparatus used to create an annular oil macrlm for ultrasonic-redegection experiments

film

thic

knes

s (m

m)

100

90

80

70

60

50

40

30

20

10

0

angular position (deg)

-180 -135 -90 -45 0 45 90 135 180

ultrasonic measurements

mathematical solution

Figure 10 Film-thickness values measured by ultrasonic redegection for an annular macrlm betweentwo eccentric cylinders Experimental results are compared with the geometrical solution

where R1 and R2 are the radii of the bush and shaft respectively and rsquo is theangle measured from the point of contact Equation (54) is included in shygure 10 forcomparison and a good correlation was observed

To reduce the enotects of the curvature of the lubricated interface the transducersused in this experiment focus the wave onto the oil layer The spot size of the focusedwave varies with frequency according to the relationship (Silk 1984)

df(iexcl6 d B) =1028F c

fD (55)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 969

steel disc water bath

oil meniscus

rotating steel ball

transducer

hydraulic load

motor drive

Figure 11 Schematic of the experimental apparatus used to generatean EHD macrlm for a ball sliding on a degat

where df is the diameter of the spot size (where the signal has reduced to iexcl6 dBof its peak value) F is the transducer focusing length f is the wave frequencyc is the speed of sound in water and D is the diameter of the piezoelectric elementFor a 25 MHz frequency wave this corresponds to a spot size in water of 522 mmThis is small compared with the radius of the shaftbush apparatus So essentiallythe transducer is receiving signals back from a regat region of constant shylm thick-ness and the curvature has little enotect The good agreement between experimen-tal and theoretical liquid-layer thickness shown in shygure 10 further validates thishypothesis

6 Measurement of dynamic lubricating macrlms

An EHD lubricant shylm forms between rolling or sliding non-conformal contactsTypically the thickness of the oil layer is in the region of 011 mm This is withinthe range of the possible measurement by ultrasonic means and within the spring-model regime of ultrasonic response In this work EHD shylms have been measuredin a model rig containing a single stationary lubricated contact and in a rolling-element bearing where the lubricant shylm is transient (with respect to the trans-ducer)

(a) Ball on disc EHD lubrication apparatus

Figure 11 shows the apparatus used to generate a single EHD lubricated contactA steel ball is supported on rollers and hydraulically loaded onto the underside ofa steel disc The ball is rotated at constant speed by an electric motor througha gear box and quill shaft The steel disc is held stationary such that the ball iscompletely sliding against the underside of the disc This apparatus is a modishyed`optical elastohydrodynamicrsquo apparatus (originally developed by Cameron amp Gohar(1966)) where the semi-reregective rotating glass disc has been replaced by a station-

Proc R Soc Lond A (2003)

970 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

005

010

015

020

025

030

035

040

0 02 04 06 08 10 12 14

lubri

can

t fi

lm thic

kness

(m

m)

entrainment speed (m s-1)

theoretical solution a = 015 mmmeasurements a = 015 mmtheoretical solution a = 01 mmmeasurements a = 01 mm

Figure 12 EHD lubricant-macrlm-thickness variation with ball-sliding speed for two loadsUltrasonic-redegection measurements are compared with a theoretical solution

ary steel disc and the microscope replaced by an ultrasonic transducer The balldisc contact was regooded with a mineral oil (Shell Turbo T68) which is entrainedinto the contact to form an EHD shylm A 50 MHz focused transducer was mountedabove the contact in a water bath The transducer was positioned directly abovethe contact region and at a distance such that the wave is focused on the balldiscinterface

Reregected pulses were recorded from the discball interface as the ball rotationalspeed and load were varied A reference spectrum was obtained by recording the pulsereregected when the ball was out of contact with the disc but the disc was still regoodedwith oil As in the wedge experiment the reference and lubricant-layer measurementswere used in (32) to obtain the reregection-coemacrcient spectrum of the lubricant layerA series of reregection coemacrcient spectra were then recorded from the discball contactas the sliding speed was increased The spring model (equation (27)) was used todetermine the shylm thickness from these spectra An automated LabView interfacewas written to record the spectra divide by a reference and convert the data intoshylm thickness (as shown in shygure 6) As discussed in x 3 above the density and speedof sound of the oil used in (27) are those at contact pressure (in this case 08 GPa)and not those in the bulk

Figure 12 shows the measured variation in shylm thickness determined from thereregection coemacrcient spectra as the speed is increased for two load cases (giving con-tact radii a of 01 and 015 mm) For this lubrication case a theoretical predictionof the oil-shylm thickness can be obtained from the regression equations of Dowson ampHigginson (1966) The central shylm thickness hc is expressed as a regression equationconsisting of shyve non-dimensional parameters

Hc = 269U 067G053W iexcl0067(1 iexcl 061eiexcl073k) (61)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 971

test rolling bearing

measurement zone

hydraulic loading

focusing transducer

water bath

belt and pulley drive

Figure 13 Schematic of apparatus used for ultrasonic measurementsof macrlm thickness in rolling-element bearings

where

Hc =hc

Rx

W =P

2EcurrenR2x

U =sup20u

2EcurrenRx

k = 103

micro

Ry

Rx

para064

G = 2notEcurren

where Ecurren is the reduced modulus Rx and Ry are the reduced radii in the paralleland transverse directions u is the mean surface speed P is the applied contact loadsup20 is the viscosity of oil in the inlet and not is its pressure-viscosity coemacrcient

The predictions of (61) for the two load cases are plotted in shygure 12 The agree-ment between the theoretical solution and the experimental data is good Typicallythe measured data are repeatable to within sect20 The oil shylm generated by theapparatus is not completely stable To directly observe the lubricant shylm the steeldisc was replaced by the glass disc and the shylm monitored visually A certain amountof shylm reguctuation was observed during normal running (caused by a slight processingof the ball on its supporting rollers) Notwithstanding the results are encouragingbecause this indicates that both the integrity of the ultrasonic method and alsothat the speed of sound of the lubricating oil compares well with predictions fromhigh-pressure measurements

(b) Rolling bearing lubricant-macrlm measurement

The duration of the ultrasonic pulses used in this work was short Spatially thepulse width was typically three wavelengths in length A 25 MHz wave travelling insteel results in a pulse duration of 01 ms Therefore it is feasible to record the shylmthickness in a rolling element moving past the focal point of an ultrasonic transducer

The approach has been used to measure shylm thickness in a 6410 deep-grooveball bearing Figure 13 shows a schematic of the bearing and the positioning of thetransducer The 25 MHz transducer (see table 2 for details) was located in a small

Proc R Soc Lond A (2003)

972 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

0

01

02

03

04

05

07

01 02 03 04 05 06 07

theo

reti

cal

film

thic

knes

s pre

dic

tion (

mm

)

45 kN 112 RPM 60 kN 72 RPM

60 kN 103 RPM 60 kN 128 RPM

60 kN 135 RPM 60 kN 137 RPM

60 kN 178 RPM 60 kN 195 RPM

60 kN 297 RPM 60 kN 375 RPM

75 kN 48 RPM 75 kN 124 RPM

06

measured film thickness (mm)

Figure 14 Comparison of rolling-element-bearing macrlm thickness measured byan ultrasonic means with EHD theoretical solution

water bath machined out of the bearing bush The transducer was spherically focusedand positioned in the water bath so that the wave was focused on the contact betweena ball and the raceway The bearing was loaded hydraulically and rotated by anelectric motor The bearing cavity was regooded with a mineral oil (Shell Turbo T68) Athermocouple was positioned on the outer raceway near the ultrasonic measurementpoint The bearing was loaded to give a contact eclipse between the ball and theouter raceway of semi-major and semi-minor axes 115 and 08 mm respectivelyThe bearing was then rotated and the transducer set to continuously pulse at arepetition rate of 10 kHz

The focal spot size of the transducer was ca 500 mm The maximum rotationalspeed of the bearing in these tests was 375 rpm At this rotational speed theregion of focused ultrasound would remain completely within the lubricated con-tact for ca 05 ms This allowed approximately shyve discrete pulses of ultrasound tobe reregected from the lubricant shylm as each ball passed through the measurementzone Initially a reference reregected pulse was recorded when the bearing was station-ary and there was no ball located over the measurement zone (although the cavitywas still shylled with oil) If a pulse is incident on an EHD shylm its amplitude is reducedbecause part of the wave has been transmitted through the oil shylm into the ball Bycontinuously monitoring the signals reregected from the raceway measurements of theball-raceway contacts were made Of the shyve pulses reregected from the ball-racewaycontact the lowest amplitude pulse was selected for analysis This pulse correspondsto the thinnest measured shylm thickness It should be noted that the resolution of thefocused transducer and the measurement interval are such that it was not possibleto record the horseshoe-shaped minimum shylm-thickness constriction at the contactexit The selected pulse was analysed shyrstly using (53) to calculate the reregection

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 973

film

thic

knes

s (m

m)

1000

100

10

1

01

001

00010 10 20 30 40 50 60

f (MHz)

time of flight limit

resonance method limit

spring model upper limit (R = 09)

spring model lower limit (R = 01)

Figure 15 Limits of operation for macrlm-thickness measurement by ultrasonic means

coemacrcient and then using the spring model to predict the shylm thickness The speedof sound in the oil in the contact is set to c = 4400 m siexcl1 (determined using themethod described in x 3)

Figure 14 shows the measured shylm thickness plotted against a prediction of theshylm thickness from the solution for an elliptical contact of Dowson amp Higginson(1966) (equation (61)) The bearing and lubricant heats up during operation Thetemperature of the entrained oil was monitored and used to determine an appropriateviscosity with which to calculate the shylm thickness in (61) This was why the resultswere not plotted as shylm thickness against speed (as in shygure 11) because viscositywas varying throughout the test

The results in shygure 14 show good agreement between measured lubricant-shylmthickness and that predicted by the EHD regression equations The spread along thex-axis shows the variation in shylm for nominally the same bearing operating conditions(load speed and oil temperature) At this stage it is not clear whether this scatteris a result of the measurement process or whether this is the actual shylm thicknessin the bearing It is worth noting that this measurement process could be improvedif the exact position of the ball could be related to the ultrasonic measurement soallowing a more precise measurement of the minimum shylm thickness

7 Discussion limits of operation

It is instructive to consider the limits of shylm-thickness measurement for a given ultra-sonic frequency The simplest method for determining the thickness of a lubricantlayer providing it is sumacrciently thick is by measuring the ToF through the layerA reregection occurs at the layer front face and another at the back face The thick-ness is readily obtained from the time between the arrival of these pulses multipliedby the acoustic velocity For the method to work the two reregected pulses must besumacrciently discrete and so the propagation distance must be greater than the pulse

Proc R Soc Lond A (2003)

974 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

width and so the minimum shylm thickness detectable by this method is given by

h gtnc

2f (71)

where n is the number of wavelengths in the ultrasonic pulse typically around threeThis measurement limit is plotted in shygure 15 as the minimum frequency requiredto measure a given shylm thickness Conventional ultrasonic non-destructive testingis generally restricted by losses in the propagating media (steel in this case) tofrequencies below 4060 MHz From (71) this means that the ToF method is onlypractically useful for layers of thickness greater than 40 mm This is thicker than thatfound on most commercial bearing systems

A lubricant layer resonates at a frequency given by (23) This equation also givesthe low thickness limit for this technique as the upper frequency output by a giventransducer determined the lowest measurable layer thickness This limit is also shownin shygure 15 for the shyrst through-thickness mode (ie m = 1) So using the highestpractical frequencies shylms greater than 10 mm are measurable by the shylm-resonancemethod

The upper limit of shylm thickness measurable using the spring-model approach isreached as R tends to unity in (27) Experience shows that measurements of R lessthan 09 yield satisfactory results The lowest shylm thickness measurable will dependon the smallest possible value of R This in turn will depend on the signal-to-noiseratio A signal-to-noise ratio of 60 dB is typical for conventional ultrasonic non-destructive testing systems The noise amplitude is thus 1

1000of the pulse amplitude

In the case of a measurement on a real bearing the achievable signal-to-noise ratiowill be reduced by the transducer-bearing reregection coemacrcient and by the attenuationin the bearing shell This means that the pulse incident in the reguid shylm will bereduced from that output by the transducer by a factor of shyve (as a conservativeestimate) Further it is assumed that for reliable measurements a pulse reregectedfrom the oil layer should have an amplitude approximately 20 times that of the noiselevel This results in a minimum measurable reregection coemacrcient of R = 01 Therelationships between the shylm thickness and the transducer frequency for the upperlimit when R = 09 and the lower where R = 01 are shown in shygure 15

This indicates that for a measuring frequency of 60 MHz a lubricant shylm of 2 nmis measurable This opens up the possibility of measuring boundary-type lubricantshylms between machine elements However the models presented here are designedfor a parallel-sided oil layer completely separating the smooth bearing surface If atthese low shylm thickness metal-to-metal contact occurs then transmission will occurat this location In this case some alternative method for interpreting reregectioncoemacrcients will be needed

8 Conclusions

Ultrasound is reregected from the lubricant shylm between bearing surfaces It is possibleto deduce the thickness of the lubricant shylm by comparing the frequency spectrumof the reregected pulse with that of the incident pulse The response of the lubricantlayer to an ultrasonic pulse has been modelled using both a spring-model methodand a continuum method The spring model is suitable for thin lubricant shylms inwhich the wavelength of the ultrasound is much larger than the layer thickness The

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 975

continuum model is valid for all layer thicknesses and allows the prediction of thethrough-thickness resonant frequencies of the lubricant layers Measurement of thesethrough-thickness resonances also provides a means of measuring the layer thickness

Experiments on reguid layers between regat plates and eccentric rings have demon-strated that ultrasound can suitably measure a wide range of liquid layer thicknessThe EHD lubricant shylm that forms between a ball sliding on a regat surface hasalso been measured ultrasonically The measured results agree well with theoreti-cal predictions taking into account the greatly increased speed of sound throughthe lubricant when it is under high pressure Films in the range 50500 nm wererecorded

The approach can also be used to measure shylm thickness in a rolling-elementbearing An ultrasonic transducer was mounted on the bearing raceway and thepulse reregected from the lubricant layer generated as the ball passes was recordedAgain measured results agreed well with theoretical predictions

The lower limit of measurement by this method depends on the signal-to-noiseratio A continuum model showed that using frequencies up to 60 MHz permits themeasurement of 2 nm thick shylms There is no upper limit to shylm-thickness measure-ment Thick shylms (greater than 40 mm) can be measured by a time-of-regight methodFilms of intermediate thickness can be determined by measuring the frequency atwhich the shylm resonates

This work was funded by a grant from the UK Engineering and Physical Sciences ResearchCouncil under the ROPA programme The authors acknowledge the help of Phil Harper of theUniversity of Sheplusmneld for his assistance with some of the measurements

References

Astridge D G amp Longmacreld M D 1967 Capacitance measurement and oil macrlm thickness in alarge radius disc and ring machine Proc Inst Mech Engrs 182 8996

Cameron A amp Gohar R 1966 Theoretical and experimental studies of the oil macrlm in lubricatedpoint contact Proc R Soc Lond A 291 520536

Dowson D amp Higginson G R 1966 Elastohydrodynamic lubrication|the fundamentals of roller

and gear lubrication Oxford Pergamon

Drinkwater B W Dwyer-Joyce R S amp Cawley P 1996 A study of the interaction betweenultrasound and a partially contacting solidsolid interface Proc R Soc Lond A 452 26132628

El-Sisi S I amp Shawki G S A 1960 Measurement of oil-macrlm thickness between disks by electricalconductivity Trans ASME J Basic Engng 82 12

Hamilton G M amp Moore S L 1967 A modimacred gauge for investigating an elastohydrodynamiccontact Proc Inst Mech Engrs 182 251

Hamrock B J 1994 Fundamentals of deguid macrlm lubrication McGraw-Hill

Hosten B 1991 Bulk heterogeneous plane-wave propagation through viscoelastic plates andstratimacred media with large values of frequency-domain Ultrasonics 29 445450

Jacobson B O amp Vinet P 1987 A model for the indeguence of pressure on the bulk modulusand the indeguence of temperature on the solidimacrcation pressure for liquid lubricants Trans

ASME J Tribology 109 709

Johnston G J Wayte R amp Spikes H A 1991 The measurement and study of very thinlubricant macrlms in concentrated contacts Tribol Trans 34 187194

Kinra V K Jaminet P T Zhu C amp Iyer V R 1994 Simultaneous measurement of theacoustical properties of a thin-layered medium the inverse problem J Acoust Soc Am 9530593074

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 969

steel disc water bath

oil meniscus

rotating steel ball

transducer

hydraulic load

motor drive

Figure 11 Schematic of the experimental apparatus used to generatean EHD macrlm for a ball sliding on a degat

where df is the diameter of the spot size (where the signal has reduced to iexcl6 dBof its peak value) F is the transducer focusing length f is the wave frequencyc is the speed of sound in water and D is the diameter of the piezoelectric elementFor a 25 MHz frequency wave this corresponds to a spot size in water of 522 mmThis is small compared with the radius of the shaftbush apparatus So essentiallythe transducer is receiving signals back from a regat region of constant shylm thick-ness and the curvature has little enotect The good agreement between experimen-tal and theoretical liquid-layer thickness shown in shygure 10 further validates thishypothesis

6 Measurement of dynamic lubricating macrlms

An EHD lubricant shylm forms between rolling or sliding non-conformal contactsTypically the thickness of the oil layer is in the region of 011 mm This is withinthe range of the possible measurement by ultrasonic means and within the spring-model regime of ultrasonic response In this work EHD shylms have been measuredin a model rig containing a single stationary lubricated contact and in a rolling-element bearing where the lubricant shylm is transient (with respect to the trans-ducer)

(a) Ball on disc EHD lubrication apparatus

Figure 11 shows the apparatus used to generate a single EHD lubricated contactA steel ball is supported on rollers and hydraulically loaded onto the underside ofa steel disc The ball is rotated at constant speed by an electric motor througha gear box and quill shaft The steel disc is held stationary such that the ball iscompletely sliding against the underside of the disc This apparatus is a modishyed`optical elastohydrodynamicrsquo apparatus (originally developed by Cameron amp Gohar(1966)) where the semi-reregective rotating glass disc has been replaced by a station-

Proc R Soc Lond A (2003)

970 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

005

010

015

020

025

030

035

040

0 02 04 06 08 10 12 14

lubri

can

t fi

lm thic

kness

(m

m)

entrainment speed (m s-1)

theoretical solution a = 015 mmmeasurements a = 015 mmtheoretical solution a = 01 mmmeasurements a = 01 mm

Figure 12 EHD lubricant-macrlm-thickness variation with ball-sliding speed for two loadsUltrasonic-redegection measurements are compared with a theoretical solution

ary steel disc and the microscope replaced by an ultrasonic transducer The balldisc contact was regooded with a mineral oil (Shell Turbo T68) which is entrainedinto the contact to form an EHD shylm A 50 MHz focused transducer was mountedabove the contact in a water bath The transducer was positioned directly abovethe contact region and at a distance such that the wave is focused on the balldiscinterface

Reregected pulses were recorded from the discball interface as the ball rotationalspeed and load were varied A reference spectrum was obtained by recording the pulsereregected when the ball was out of contact with the disc but the disc was still regoodedwith oil As in the wedge experiment the reference and lubricant-layer measurementswere used in (32) to obtain the reregection-coemacrcient spectrum of the lubricant layerA series of reregection coemacrcient spectra were then recorded from the discball contactas the sliding speed was increased The spring model (equation (27)) was used todetermine the shylm thickness from these spectra An automated LabView interfacewas written to record the spectra divide by a reference and convert the data intoshylm thickness (as shown in shygure 6) As discussed in x 3 above the density and speedof sound of the oil used in (27) are those at contact pressure (in this case 08 GPa)and not those in the bulk

Figure 12 shows the measured variation in shylm thickness determined from thereregection coemacrcient spectra as the speed is increased for two load cases (giving con-tact radii a of 01 and 015 mm) For this lubrication case a theoretical predictionof the oil-shylm thickness can be obtained from the regression equations of Dowson ampHigginson (1966) The central shylm thickness hc is expressed as a regression equationconsisting of shyve non-dimensional parameters

Hc = 269U 067G053W iexcl0067(1 iexcl 061eiexcl073k) (61)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 971

test rolling bearing

measurement zone

hydraulic loading

focusing transducer

water bath

belt and pulley drive

Figure 13 Schematic of apparatus used for ultrasonic measurementsof macrlm thickness in rolling-element bearings

where

Hc =hc

Rx

W =P

2EcurrenR2x

U =sup20u

2EcurrenRx

k = 103

micro

Ry

Rx

para064

G = 2notEcurren

where Ecurren is the reduced modulus Rx and Ry are the reduced radii in the paralleland transverse directions u is the mean surface speed P is the applied contact loadsup20 is the viscosity of oil in the inlet and not is its pressure-viscosity coemacrcient

The predictions of (61) for the two load cases are plotted in shygure 12 The agree-ment between the theoretical solution and the experimental data is good Typicallythe measured data are repeatable to within sect20 The oil shylm generated by theapparatus is not completely stable To directly observe the lubricant shylm the steeldisc was replaced by the glass disc and the shylm monitored visually A certain amountof shylm reguctuation was observed during normal running (caused by a slight processingof the ball on its supporting rollers) Notwithstanding the results are encouragingbecause this indicates that both the integrity of the ultrasonic method and alsothat the speed of sound of the lubricating oil compares well with predictions fromhigh-pressure measurements

(b) Rolling bearing lubricant-macrlm measurement

The duration of the ultrasonic pulses used in this work was short Spatially thepulse width was typically three wavelengths in length A 25 MHz wave travelling insteel results in a pulse duration of 01 ms Therefore it is feasible to record the shylmthickness in a rolling element moving past the focal point of an ultrasonic transducer

The approach has been used to measure shylm thickness in a 6410 deep-grooveball bearing Figure 13 shows a schematic of the bearing and the positioning of thetransducer The 25 MHz transducer (see table 2 for details) was located in a small

Proc R Soc Lond A (2003)

972 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

0

01

02

03

04

05

07

01 02 03 04 05 06 07

theo

reti

cal

film

thic

knes

s pre

dic

tion (

mm

)

45 kN 112 RPM 60 kN 72 RPM

60 kN 103 RPM 60 kN 128 RPM

60 kN 135 RPM 60 kN 137 RPM

60 kN 178 RPM 60 kN 195 RPM

60 kN 297 RPM 60 kN 375 RPM

75 kN 48 RPM 75 kN 124 RPM

06

measured film thickness (mm)

Figure 14 Comparison of rolling-element-bearing macrlm thickness measured byan ultrasonic means with EHD theoretical solution

water bath machined out of the bearing bush The transducer was spherically focusedand positioned in the water bath so that the wave was focused on the contact betweena ball and the raceway The bearing was loaded hydraulically and rotated by anelectric motor The bearing cavity was regooded with a mineral oil (Shell Turbo T68) Athermocouple was positioned on the outer raceway near the ultrasonic measurementpoint The bearing was loaded to give a contact eclipse between the ball and theouter raceway of semi-major and semi-minor axes 115 and 08 mm respectivelyThe bearing was then rotated and the transducer set to continuously pulse at arepetition rate of 10 kHz

The focal spot size of the transducer was ca 500 mm The maximum rotationalspeed of the bearing in these tests was 375 rpm At this rotational speed theregion of focused ultrasound would remain completely within the lubricated con-tact for ca 05 ms This allowed approximately shyve discrete pulses of ultrasound tobe reregected from the lubricant shylm as each ball passed through the measurementzone Initially a reference reregected pulse was recorded when the bearing was station-ary and there was no ball located over the measurement zone (although the cavitywas still shylled with oil) If a pulse is incident on an EHD shylm its amplitude is reducedbecause part of the wave has been transmitted through the oil shylm into the ball Bycontinuously monitoring the signals reregected from the raceway measurements of theball-raceway contacts were made Of the shyve pulses reregected from the ball-racewaycontact the lowest amplitude pulse was selected for analysis This pulse correspondsto the thinnest measured shylm thickness It should be noted that the resolution of thefocused transducer and the measurement interval are such that it was not possibleto record the horseshoe-shaped minimum shylm-thickness constriction at the contactexit The selected pulse was analysed shyrstly using (53) to calculate the reregection

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 973

film

thic

knes

s (m

m)

1000

100

10

1

01

001

00010 10 20 30 40 50 60

f (MHz)

time of flight limit

resonance method limit

spring model upper limit (R = 09)

spring model lower limit (R = 01)

Figure 15 Limits of operation for macrlm-thickness measurement by ultrasonic means

coemacrcient and then using the spring model to predict the shylm thickness The speedof sound in the oil in the contact is set to c = 4400 m siexcl1 (determined using themethod described in x 3)

Figure 14 shows the measured shylm thickness plotted against a prediction of theshylm thickness from the solution for an elliptical contact of Dowson amp Higginson(1966) (equation (61)) The bearing and lubricant heats up during operation Thetemperature of the entrained oil was monitored and used to determine an appropriateviscosity with which to calculate the shylm thickness in (61) This was why the resultswere not plotted as shylm thickness against speed (as in shygure 11) because viscositywas varying throughout the test

The results in shygure 14 show good agreement between measured lubricant-shylmthickness and that predicted by the EHD regression equations The spread along thex-axis shows the variation in shylm for nominally the same bearing operating conditions(load speed and oil temperature) At this stage it is not clear whether this scatteris a result of the measurement process or whether this is the actual shylm thicknessin the bearing It is worth noting that this measurement process could be improvedif the exact position of the ball could be related to the ultrasonic measurement soallowing a more precise measurement of the minimum shylm thickness

7 Discussion limits of operation

It is instructive to consider the limits of shylm-thickness measurement for a given ultra-sonic frequency The simplest method for determining the thickness of a lubricantlayer providing it is sumacrciently thick is by measuring the ToF through the layerA reregection occurs at the layer front face and another at the back face The thick-ness is readily obtained from the time between the arrival of these pulses multipliedby the acoustic velocity For the method to work the two reregected pulses must besumacrciently discrete and so the propagation distance must be greater than the pulse

Proc R Soc Lond A (2003)

974 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

width and so the minimum shylm thickness detectable by this method is given by

h gtnc

2f (71)

where n is the number of wavelengths in the ultrasonic pulse typically around threeThis measurement limit is plotted in shygure 15 as the minimum frequency requiredto measure a given shylm thickness Conventional ultrasonic non-destructive testingis generally restricted by losses in the propagating media (steel in this case) tofrequencies below 4060 MHz From (71) this means that the ToF method is onlypractically useful for layers of thickness greater than 40 mm This is thicker than thatfound on most commercial bearing systems

A lubricant layer resonates at a frequency given by (23) This equation also givesthe low thickness limit for this technique as the upper frequency output by a giventransducer determined the lowest measurable layer thickness This limit is also shownin shygure 15 for the shyrst through-thickness mode (ie m = 1) So using the highestpractical frequencies shylms greater than 10 mm are measurable by the shylm-resonancemethod

The upper limit of shylm thickness measurable using the spring-model approach isreached as R tends to unity in (27) Experience shows that measurements of R lessthan 09 yield satisfactory results The lowest shylm thickness measurable will dependon the smallest possible value of R This in turn will depend on the signal-to-noiseratio A signal-to-noise ratio of 60 dB is typical for conventional ultrasonic non-destructive testing systems The noise amplitude is thus 1

1000of the pulse amplitude

In the case of a measurement on a real bearing the achievable signal-to-noise ratiowill be reduced by the transducer-bearing reregection coemacrcient and by the attenuationin the bearing shell This means that the pulse incident in the reguid shylm will bereduced from that output by the transducer by a factor of shyve (as a conservativeestimate) Further it is assumed that for reliable measurements a pulse reregectedfrom the oil layer should have an amplitude approximately 20 times that of the noiselevel This results in a minimum measurable reregection coemacrcient of R = 01 Therelationships between the shylm thickness and the transducer frequency for the upperlimit when R = 09 and the lower where R = 01 are shown in shygure 15

This indicates that for a measuring frequency of 60 MHz a lubricant shylm of 2 nmis measurable This opens up the possibility of measuring boundary-type lubricantshylms between machine elements However the models presented here are designedfor a parallel-sided oil layer completely separating the smooth bearing surface If atthese low shylm thickness metal-to-metal contact occurs then transmission will occurat this location In this case some alternative method for interpreting reregectioncoemacrcients will be needed

8 Conclusions

Ultrasound is reregected from the lubricant shylm between bearing surfaces It is possibleto deduce the thickness of the lubricant shylm by comparing the frequency spectrumof the reregected pulse with that of the incident pulse The response of the lubricantlayer to an ultrasonic pulse has been modelled using both a spring-model methodand a continuum method The spring model is suitable for thin lubricant shylms inwhich the wavelength of the ultrasound is much larger than the layer thickness The

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 975

continuum model is valid for all layer thicknesses and allows the prediction of thethrough-thickness resonant frequencies of the lubricant layers Measurement of thesethrough-thickness resonances also provides a means of measuring the layer thickness

Experiments on reguid layers between regat plates and eccentric rings have demon-strated that ultrasound can suitably measure a wide range of liquid layer thicknessThe EHD lubricant shylm that forms between a ball sliding on a regat surface hasalso been measured ultrasonically The measured results agree well with theoreti-cal predictions taking into account the greatly increased speed of sound throughthe lubricant when it is under high pressure Films in the range 50500 nm wererecorded

The approach can also be used to measure shylm thickness in a rolling-elementbearing An ultrasonic transducer was mounted on the bearing raceway and thepulse reregected from the lubricant layer generated as the ball passes was recordedAgain measured results agreed well with theoretical predictions

The lower limit of measurement by this method depends on the signal-to-noiseratio A continuum model showed that using frequencies up to 60 MHz permits themeasurement of 2 nm thick shylms There is no upper limit to shylm-thickness measure-ment Thick shylms (greater than 40 mm) can be measured by a time-of-regight methodFilms of intermediate thickness can be determined by measuring the frequency atwhich the shylm resonates

This work was funded by a grant from the UK Engineering and Physical Sciences ResearchCouncil under the ROPA programme The authors acknowledge the help of Phil Harper of theUniversity of Sheplusmneld for his assistance with some of the measurements

References

Astridge D G amp Longmacreld M D 1967 Capacitance measurement and oil macrlm thickness in alarge radius disc and ring machine Proc Inst Mech Engrs 182 8996

Cameron A amp Gohar R 1966 Theoretical and experimental studies of the oil macrlm in lubricatedpoint contact Proc R Soc Lond A 291 520536

Dowson D amp Higginson G R 1966 Elastohydrodynamic lubrication|the fundamentals of roller

and gear lubrication Oxford Pergamon

Drinkwater B W Dwyer-Joyce R S amp Cawley P 1996 A study of the interaction betweenultrasound and a partially contacting solidsolid interface Proc R Soc Lond A 452 26132628

El-Sisi S I amp Shawki G S A 1960 Measurement of oil-macrlm thickness between disks by electricalconductivity Trans ASME J Basic Engng 82 12

Hamilton G M amp Moore S L 1967 A modimacred gauge for investigating an elastohydrodynamiccontact Proc Inst Mech Engrs 182 251

Hamrock B J 1994 Fundamentals of deguid macrlm lubrication McGraw-Hill

Hosten B 1991 Bulk heterogeneous plane-wave propagation through viscoelastic plates andstratimacred media with large values of frequency-domain Ultrasonics 29 445450

Jacobson B O amp Vinet P 1987 A model for the indeguence of pressure on the bulk modulusand the indeguence of temperature on the solidimacrcation pressure for liquid lubricants Trans

ASME J Tribology 109 709

Johnston G J Wayte R amp Spikes H A 1991 The measurement and study of very thinlubricant macrlms in concentrated contacts Tribol Trans 34 187194

Kinra V K Jaminet P T Zhu C amp Iyer V R 1994 Simultaneous measurement of theacoustical properties of a thin-layered medium the inverse problem J Acoust Soc Am 9530593074

Proc R Soc Lond A (2003)

970 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

005

010

015

020

025

030

035

040

0 02 04 06 08 10 12 14

lubri

can

t fi

lm thic

kness

(m

m)

entrainment speed (m s-1)

theoretical solution a = 015 mmmeasurements a = 015 mmtheoretical solution a = 01 mmmeasurements a = 01 mm

Figure 12 EHD lubricant-macrlm-thickness variation with ball-sliding speed for two loadsUltrasonic-redegection measurements are compared with a theoretical solution

ary steel disc and the microscope replaced by an ultrasonic transducer The balldisc contact was regooded with a mineral oil (Shell Turbo T68) which is entrainedinto the contact to form an EHD shylm A 50 MHz focused transducer was mountedabove the contact in a water bath The transducer was positioned directly abovethe contact region and at a distance such that the wave is focused on the balldiscinterface

Reregected pulses were recorded from the discball interface as the ball rotationalspeed and load were varied A reference spectrum was obtained by recording the pulsereregected when the ball was out of contact with the disc but the disc was still regoodedwith oil As in the wedge experiment the reference and lubricant-layer measurementswere used in (32) to obtain the reregection-coemacrcient spectrum of the lubricant layerA series of reregection coemacrcient spectra were then recorded from the discball contactas the sliding speed was increased The spring model (equation (27)) was used todetermine the shylm thickness from these spectra An automated LabView interfacewas written to record the spectra divide by a reference and convert the data intoshylm thickness (as shown in shygure 6) As discussed in x 3 above the density and speedof sound of the oil used in (27) are those at contact pressure (in this case 08 GPa)and not those in the bulk

Figure 12 shows the measured variation in shylm thickness determined from thereregection coemacrcient spectra as the speed is increased for two load cases (giving con-tact radii a of 01 and 015 mm) For this lubrication case a theoretical predictionof the oil-shylm thickness can be obtained from the regression equations of Dowson ampHigginson (1966) The central shylm thickness hc is expressed as a regression equationconsisting of shyve non-dimensional parameters

Hc = 269U 067G053W iexcl0067(1 iexcl 061eiexcl073k) (61)

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 971

test rolling bearing

measurement zone

hydraulic loading

focusing transducer

water bath

belt and pulley drive

Figure 13 Schematic of apparatus used for ultrasonic measurementsof macrlm thickness in rolling-element bearings

where

Hc =hc

Rx

W =P

2EcurrenR2x

U =sup20u

2EcurrenRx

k = 103

micro

Ry

Rx

para064

G = 2notEcurren

where Ecurren is the reduced modulus Rx and Ry are the reduced radii in the paralleland transverse directions u is the mean surface speed P is the applied contact loadsup20 is the viscosity of oil in the inlet and not is its pressure-viscosity coemacrcient

The predictions of (61) for the two load cases are plotted in shygure 12 The agree-ment between the theoretical solution and the experimental data is good Typicallythe measured data are repeatable to within sect20 The oil shylm generated by theapparatus is not completely stable To directly observe the lubricant shylm the steeldisc was replaced by the glass disc and the shylm monitored visually A certain amountof shylm reguctuation was observed during normal running (caused by a slight processingof the ball on its supporting rollers) Notwithstanding the results are encouragingbecause this indicates that both the integrity of the ultrasonic method and alsothat the speed of sound of the lubricating oil compares well with predictions fromhigh-pressure measurements

(b) Rolling bearing lubricant-macrlm measurement

The duration of the ultrasonic pulses used in this work was short Spatially thepulse width was typically three wavelengths in length A 25 MHz wave travelling insteel results in a pulse duration of 01 ms Therefore it is feasible to record the shylmthickness in a rolling element moving past the focal point of an ultrasonic transducer

The approach has been used to measure shylm thickness in a 6410 deep-grooveball bearing Figure 13 shows a schematic of the bearing and the positioning of thetransducer The 25 MHz transducer (see table 2 for details) was located in a small

Proc R Soc Lond A (2003)

972 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

0

01

02

03

04

05

07

01 02 03 04 05 06 07

theo

reti

cal

film

thic

knes

s pre

dic

tion (

mm

)

45 kN 112 RPM 60 kN 72 RPM

60 kN 103 RPM 60 kN 128 RPM

60 kN 135 RPM 60 kN 137 RPM

60 kN 178 RPM 60 kN 195 RPM

60 kN 297 RPM 60 kN 375 RPM

75 kN 48 RPM 75 kN 124 RPM

06

measured film thickness (mm)

Figure 14 Comparison of rolling-element-bearing macrlm thickness measured byan ultrasonic means with EHD theoretical solution

water bath machined out of the bearing bush The transducer was spherically focusedand positioned in the water bath so that the wave was focused on the contact betweena ball and the raceway The bearing was loaded hydraulically and rotated by anelectric motor The bearing cavity was regooded with a mineral oil (Shell Turbo T68) Athermocouple was positioned on the outer raceway near the ultrasonic measurementpoint The bearing was loaded to give a contact eclipse between the ball and theouter raceway of semi-major and semi-minor axes 115 and 08 mm respectivelyThe bearing was then rotated and the transducer set to continuously pulse at arepetition rate of 10 kHz

The focal spot size of the transducer was ca 500 mm The maximum rotationalspeed of the bearing in these tests was 375 rpm At this rotational speed theregion of focused ultrasound would remain completely within the lubricated con-tact for ca 05 ms This allowed approximately shyve discrete pulses of ultrasound tobe reregected from the lubricant shylm as each ball passed through the measurementzone Initially a reference reregected pulse was recorded when the bearing was station-ary and there was no ball located over the measurement zone (although the cavitywas still shylled with oil) If a pulse is incident on an EHD shylm its amplitude is reducedbecause part of the wave has been transmitted through the oil shylm into the ball Bycontinuously monitoring the signals reregected from the raceway measurements of theball-raceway contacts were made Of the shyve pulses reregected from the ball-racewaycontact the lowest amplitude pulse was selected for analysis This pulse correspondsto the thinnest measured shylm thickness It should be noted that the resolution of thefocused transducer and the measurement interval are such that it was not possibleto record the horseshoe-shaped minimum shylm-thickness constriction at the contactexit The selected pulse was analysed shyrstly using (53) to calculate the reregection

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 973

film

thic

knes

s (m

m)

1000

100

10

1

01

001

00010 10 20 30 40 50 60

f (MHz)

time of flight limit

resonance method limit

spring model upper limit (R = 09)

spring model lower limit (R = 01)

Figure 15 Limits of operation for macrlm-thickness measurement by ultrasonic means

coemacrcient and then using the spring model to predict the shylm thickness The speedof sound in the oil in the contact is set to c = 4400 m siexcl1 (determined using themethod described in x 3)

Figure 14 shows the measured shylm thickness plotted against a prediction of theshylm thickness from the solution for an elliptical contact of Dowson amp Higginson(1966) (equation (61)) The bearing and lubricant heats up during operation Thetemperature of the entrained oil was monitored and used to determine an appropriateviscosity with which to calculate the shylm thickness in (61) This was why the resultswere not plotted as shylm thickness against speed (as in shygure 11) because viscositywas varying throughout the test

The results in shygure 14 show good agreement between measured lubricant-shylmthickness and that predicted by the EHD regression equations The spread along thex-axis shows the variation in shylm for nominally the same bearing operating conditions(load speed and oil temperature) At this stage it is not clear whether this scatteris a result of the measurement process or whether this is the actual shylm thicknessin the bearing It is worth noting that this measurement process could be improvedif the exact position of the ball could be related to the ultrasonic measurement soallowing a more precise measurement of the minimum shylm thickness

7 Discussion limits of operation

It is instructive to consider the limits of shylm-thickness measurement for a given ultra-sonic frequency The simplest method for determining the thickness of a lubricantlayer providing it is sumacrciently thick is by measuring the ToF through the layerA reregection occurs at the layer front face and another at the back face The thick-ness is readily obtained from the time between the arrival of these pulses multipliedby the acoustic velocity For the method to work the two reregected pulses must besumacrciently discrete and so the propagation distance must be greater than the pulse

Proc R Soc Lond A (2003)

974 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

width and so the minimum shylm thickness detectable by this method is given by

h gtnc

2f (71)

where n is the number of wavelengths in the ultrasonic pulse typically around threeThis measurement limit is plotted in shygure 15 as the minimum frequency requiredto measure a given shylm thickness Conventional ultrasonic non-destructive testingis generally restricted by losses in the propagating media (steel in this case) tofrequencies below 4060 MHz From (71) this means that the ToF method is onlypractically useful for layers of thickness greater than 40 mm This is thicker than thatfound on most commercial bearing systems

A lubricant layer resonates at a frequency given by (23) This equation also givesthe low thickness limit for this technique as the upper frequency output by a giventransducer determined the lowest measurable layer thickness This limit is also shownin shygure 15 for the shyrst through-thickness mode (ie m = 1) So using the highestpractical frequencies shylms greater than 10 mm are measurable by the shylm-resonancemethod

The upper limit of shylm thickness measurable using the spring-model approach isreached as R tends to unity in (27) Experience shows that measurements of R lessthan 09 yield satisfactory results The lowest shylm thickness measurable will dependon the smallest possible value of R This in turn will depend on the signal-to-noiseratio A signal-to-noise ratio of 60 dB is typical for conventional ultrasonic non-destructive testing systems The noise amplitude is thus 1

1000of the pulse amplitude

In the case of a measurement on a real bearing the achievable signal-to-noise ratiowill be reduced by the transducer-bearing reregection coemacrcient and by the attenuationin the bearing shell This means that the pulse incident in the reguid shylm will bereduced from that output by the transducer by a factor of shyve (as a conservativeestimate) Further it is assumed that for reliable measurements a pulse reregectedfrom the oil layer should have an amplitude approximately 20 times that of the noiselevel This results in a minimum measurable reregection coemacrcient of R = 01 Therelationships between the shylm thickness and the transducer frequency for the upperlimit when R = 09 and the lower where R = 01 are shown in shygure 15

This indicates that for a measuring frequency of 60 MHz a lubricant shylm of 2 nmis measurable This opens up the possibility of measuring boundary-type lubricantshylms between machine elements However the models presented here are designedfor a parallel-sided oil layer completely separating the smooth bearing surface If atthese low shylm thickness metal-to-metal contact occurs then transmission will occurat this location In this case some alternative method for interpreting reregectioncoemacrcients will be needed

8 Conclusions

Ultrasound is reregected from the lubricant shylm between bearing surfaces It is possibleto deduce the thickness of the lubricant shylm by comparing the frequency spectrumof the reregected pulse with that of the incident pulse The response of the lubricantlayer to an ultrasonic pulse has been modelled using both a spring-model methodand a continuum method The spring model is suitable for thin lubricant shylms inwhich the wavelength of the ultrasound is much larger than the layer thickness The

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 975

continuum model is valid for all layer thicknesses and allows the prediction of thethrough-thickness resonant frequencies of the lubricant layers Measurement of thesethrough-thickness resonances also provides a means of measuring the layer thickness

Experiments on reguid layers between regat plates and eccentric rings have demon-strated that ultrasound can suitably measure a wide range of liquid layer thicknessThe EHD lubricant shylm that forms between a ball sliding on a regat surface hasalso been measured ultrasonically The measured results agree well with theoreti-cal predictions taking into account the greatly increased speed of sound throughthe lubricant when it is under high pressure Films in the range 50500 nm wererecorded

The approach can also be used to measure shylm thickness in a rolling-elementbearing An ultrasonic transducer was mounted on the bearing raceway and thepulse reregected from the lubricant layer generated as the ball passes was recordedAgain measured results agreed well with theoretical predictions

The lower limit of measurement by this method depends on the signal-to-noiseratio A continuum model showed that using frequencies up to 60 MHz permits themeasurement of 2 nm thick shylms There is no upper limit to shylm-thickness measure-ment Thick shylms (greater than 40 mm) can be measured by a time-of-regight methodFilms of intermediate thickness can be determined by measuring the frequency atwhich the shylm resonates

This work was funded by a grant from the UK Engineering and Physical Sciences ResearchCouncil under the ROPA programme The authors acknowledge the help of Phil Harper of theUniversity of Sheplusmneld for his assistance with some of the measurements

References

Astridge D G amp Longmacreld M D 1967 Capacitance measurement and oil macrlm thickness in alarge radius disc and ring machine Proc Inst Mech Engrs 182 8996

Cameron A amp Gohar R 1966 Theoretical and experimental studies of the oil macrlm in lubricatedpoint contact Proc R Soc Lond A 291 520536

Dowson D amp Higginson G R 1966 Elastohydrodynamic lubrication|the fundamentals of roller

and gear lubrication Oxford Pergamon

Drinkwater B W Dwyer-Joyce R S amp Cawley P 1996 A study of the interaction betweenultrasound and a partially contacting solidsolid interface Proc R Soc Lond A 452 26132628

El-Sisi S I amp Shawki G S A 1960 Measurement of oil-macrlm thickness between disks by electricalconductivity Trans ASME J Basic Engng 82 12

Hamilton G M amp Moore S L 1967 A modimacred gauge for investigating an elastohydrodynamiccontact Proc Inst Mech Engrs 182 251

Hamrock B J 1994 Fundamentals of deguid macrlm lubrication McGraw-Hill

Hosten B 1991 Bulk heterogeneous plane-wave propagation through viscoelastic plates andstratimacred media with large values of frequency-domain Ultrasonics 29 445450

Jacobson B O amp Vinet P 1987 A model for the indeguence of pressure on the bulk modulusand the indeguence of temperature on the solidimacrcation pressure for liquid lubricants Trans

ASME J Tribology 109 709

Johnston G J Wayte R amp Spikes H A 1991 The measurement and study of very thinlubricant macrlms in concentrated contacts Tribol Trans 34 187194

Kinra V K Jaminet P T Zhu C amp Iyer V R 1994 Simultaneous measurement of theacoustical properties of a thin-layered medium the inverse problem J Acoust Soc Am 9530593074

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 971

test rolling bearing

measurement zone

hydraulic loading

focusing transducer

water bath

belt and pulley drive

Figure 13 Schematic of apparatus used for ultrasonic measurementsof macrlm thickness in rolling-element bearings

where

Hc =hc

Rx

W =P

2EcurrenR2x

U =sup20u

2EcurrenRx

k = 103

micro

Ry

Rx

para064

G = 2notEcurren

where Ecurren is the reduced modulus Rx and Ry are the reduced radii in the paralleland transverse directions u is the mean surface speed P is the applied contact loadsup20 is the viscosity of oil in the inlet and not is its pressure-viscosity coemacrcient

The predictions of (61) for the two load cases are plotted in shygure 12 The agree-ment between the theoretical solution and the experimental data is good Typicallythe measured data are repeatable to within sect20 The oil shylm generated by theapparatus is not completely stable To directly observe the lubricant shylm the steeldisc was replaced by the glass disc and the shylm monitored visually A certain amountof shylm reguctuation was observed during normal running (caused by a slight processingof the ball on its supporting rollers) Notwithstanding the results are encouragingbecause this indicates that both the integrity of the ultrasonic method and alsothat the speed of sound of the lubricating oil compares well with predictions fromhigh-pressure measurements

(b) Rolling bearing lubricant-macrlm measurement

The duration of the ultrasonic pulses used in this work was short Spatially thepulse width was typically three wavelengths in length A 25 MHz wave travelling insteel results in a pulse duration of 01 ms Therefore it is feasible to record the shylmthickness in a rolling element moving past the focal point of an ultrasonic transducer

The approach has been used to measure shylm thickness in a 6410 deep-grooveball bearing Figure 13 shows a schematic of the bearing and the positioning of thetransducer The 25 MHz transducer (see table 2 for details) was located in a small

Proc R Soc Lond A (2003)

972 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

0

01

02

03

04

05

07

01 02 03 04 05 06 07

theo

reti

cal

film

thic

knes

s pre

dic

tion (

mm

)

45 kN 112 RPM 60 kN 72 RPM

60 kN 103 RPM 60 kN 128 RPM

60 kN 135 RPM 60 kN 137 RPM

60 kN 178 RPM 60 kN 195 RPM

60 kN 297 RPM 60 kN 375 RPM

75 kN 48 RPM 75 kN 124 RPM

06

measured film thickness (mm)

Figure 14 Comparison of rolling-element-bearing macrlm thickness measured byan ultrasonic means with EHD theoretical solution

water bath machined out of the bearing bush The transducer was spherically focusedand positioned in the water bath so that the wave was focused on the contact betweena ball and the raceway The bearing was loaded hydraulically and rotated by anelectric motor The bearing cavity was regooded with a mineral oil (Shell Turbo T68) Athermocouple was positioned on the outer raceway near the ultrasonic measurementpoint The bearing was loaded to give a contact eclipse between the ball and theouter raceway of semi-major and semi-minor axes 115 and 08 mm respectivelyThe bearing was then rotated and the transducer set to continuously pulse at arepetition rate of 10 kHz

The focal spot size of the transducer was ca 500 mm The maximum rotationalspeed of the bearing in these tests was 375 rpm At this rotational speed theregion of focused ultrasound would remain completely within the lubricated con-tact for ca 05 ms This allowed approximately shyve discrete pulses of ultrasound tobe reregected from the lubricant shylm as each ball passed through the measurementzone Initially a reference reregected pulse was recorded when the bearing was station-ary and there was no ball located over the measurement zone (although the cavitywas still shylled with oil) If a pulse is incident on an EHD shylm its amplitude is reducedbecause part of the wave has been transmitted through the oil shylm into the ball Bycontinuously monitoring the signals reregected from the raceway measurements of theball-raceway contacts were made Of the shyve pulses reregected from the ball-racewaycontact the lowest amplitude pulse was selected for analysis This pulse correspondsto the thinnest measured shylm thickness It should be noted that the resolution of thefocused transducer and the measurement interval are such that it was not possibleto record the horseshoe-shaped minimum shylm-thickness constriction at the contactexit The selected pulse was analysed shyrstly using (53) to calculate the reregection

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 973

film

thic

knes

s (m

m)

1000

100

10

1

01

001

00010 10 20 30 40 50 60

f (MHz)

time of flight limit

resonance method limit

spring model upper limit (R = 09)

spring model lower limit (R = 01)

Figure 15 Limits of operation for macrlm-thickness measurement by ultrasonic means

coemacrcient and then using the spring model to predict the shylm thickness The speedof sound in the oil in the contact is set to c = 4400 m siexcl1 (determined using themethod described in x 3)

Figure 14 shows the measured shylm thickness plotted against a prediction of theshylm thickness from the solution for an elliptical contact of Dowson amp Higginson(1966) (equation (61)) The bearing and lubricant heats up during operation Thetemperature of the entrained oil was monitored and used to determine an appropriateviscosity with which to calculate the shylm thickness in (61) This was why the resultswere not plotted as shylm thickness against speed (as in shygure 11) because viscositywas varying throughout the test

The results in shygure 14 show good agreement between measured lubricant-shylmthickness and that predicted by the EHD regression equations The spread along thex-axis shows the variation in shylm for nominally the same bearing operating conditions(load speed and oil temperature) At this stage it is not clear whether this scatteris a result of the measurement process or whether this is the actual shylm thicknessin the bearing It is worth noting that this measurement process could be improvedif the exact position of the ball could be related to the ultrasonic measurement soallowing a more precise measurement of the minimum shylm thickness

7 Discussion limits of operation

It is instructive to consider the limits of shylm-thickness measurement for a given ultra-sonic frequency The simplest method for determining the thickness of a lubricantlayer providing it is sumacrciently thick is by measuring the ToF through the layerA reregection occurs at the layer front face and another at the back face The thick-ness is readily obtained from the time between the arrival of these pulses multipliedby the acoustic velocity For the method to work the two reregected pulses must besumacrciently discrete and so the propagation distance must be greater than the pulse

Proc R Soc Lond A (2003)

974 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

width and so the minimum shylm thickness detectable by this method is given by

h gtnc

2f (71)

where n is the number of wavelengths in the ultrasonic pulse typically around threeThis measurement limit is plotted in shygure 15 as the minimum frequency requiredto measure a given shylm thickness Conventional ultrasonic non-destructive testingis generally restricted by losses in the propagating media (steel in this case) tofrequencies below 4060 MHz From (71) this means that the ToF method is onlypractically useful for layers of thickness greater than 40 mm This is thicker than thatfound on most commercial bearing systems

A lubricant layer resonates at a frequency given by (23) This equation also givesthe low thickness limit for this technique as the upper frequency output by a giventransducer determined the lowest measurable layer thickness This limit is also shownin shygure 15 for the shyrst through-thickness mode (ie m = 1) So using the highestpractical frequencies shylms greater than 10 mm are measurable by the shylm-resonancemethod

The upper limit of shylm thickness measurable using the spring-model approach isreached as R tends to unity in (27) Experience shows that measurements of R lessthan 09 yield satisfactory results The lowest shylm thickness measurable will dependon the smallest possible value of R This in turn will depend on the signal-to-noiseratio A signal-to-noise ratio of 60 dB is typical for conventional ultrasonic non-destructive testing systems The noise amplitude is thus 1

1000of the pulse amplitude

In the case of a measurement on a real bearing the achievable signal-to-noise ratiowill be reduced by the transducer-bearing reregection coemacrcient and by the attenuationin the bearing shell This means that the pulse incident in the reguid shylm will bereduced from that output by the transducer by a factor of shyve (as a conservativeestimate) Further it is assumed that for reliable measurements a pulse reregectedfrom the oil layer should have an amplitude approximately 20 times that of the noiselevel This results in a minimum measurable reregection coemacrcient of R = 01 Therelationships between the shylm thickness and the transducer frequency for the upperlimit when R = 09 and the lower where R = 01 are shown in shygure 15

This indicates that for a measuring frequency of 60 MHz a lubricant shylm of 2 nmis measurable This opens up the possibility of measuring boundary-type lubricantshylms between machine elements However the models presented here are designedfor a parallel-sided oil layer completely separating the smooth bearing surface If atthese low shylm thickness metal-to-metal contact occurs then transmission will occurat this location In this case some alternative method for interpreting reregectioncoemacrcients will be needed

8 Conclusions

Ultrasound is reregected from the lubricant shylm between bearing surfaces It is possibleto deduce the thickness of the lubricant shylm by comparing the frequency spectrumof the reregected pulse with that of the incident pulse The response of the lubricantlayer to an ultrasonic pulse has been modelled using both a spring-model methodand a continuum method The spring model is suitable for thin lubricant shylms inwhich the wavelength of the ultrasound is much larger than the layer thickness The

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 975

continuum model is valid for all layer thicknesses and allows the prediction of thethrough-thickness resonant frequencies of the lubricant layers Measurement of thesethrough-thickness resonances also provides a means of measuring the layer thickness

Experiments on reguid layers between regat plates and eccentric rings have demon-strated that ultrasound can suitably measure a wide range of liquid layer thicknessThe EHD lubricant shylm that forms between a ball sliding on a regat surface hasalso been measured ultrasonically The measured results agree well with theoreti-cal predictions taking into account the greatly increased speed of sound throughthe lubricant when it is under high pressure Films in the range 50500 nm wererecorded

The approach can also be used to measure shylm thickness in a rolling-elementbearing An ultrasonic transducer was mounted on the bearing raceway and thepulse reregected from the lubricant layer generated as the ball passes was recordedAgain measured results agreed well with theoretical predictions

The lower limit of measurement by this method depends on the signal-to-noiseratio A continuum model showed that using frequencies up to 60 MHz permits themeasurement of 2 nm thick shylms There is no upper limit to shylm-thickness measure-ment Thick shylms (greater than 40 mm) can be measured by a time-of-regight methodFilms of intermediate thickness can be determined by measuring the frequency atwhich the shylm resonates

This work was funded by a grant from the UK Engineering and Physical Sciences ResearchCouncil under the ROPA programme The authors acknowledge the help of Phil Harper of theUniversity of Sheplusmneld for his assistance with some of the measurements

References

Astridge D G amp Longmacreld M D 1967 Capacitance measurement and oil macrlm thickness in alarge radius disc and ring machine Proc Inst Mech Engrs 182 8996

Cameron A amp Gohar R 1966 Theoretical and experimental studies of the oil macrlm in lubricatedpoint contact Proc R Soc Lond A 291 520536

Dowson D amp Higginson G R 1966 Elastohydrodynamic lubrication|the fundamentals of roller

and gear lubrication Oxford Pergamon

Drinkwater B W Dwyer-Joyce R S amp Cawley P 1996 A study of the interaction betweenultrasound and a partially contacting solidsolid interface Proc R Soc Lond A 452 26132628

El-Sisi S I amp Shawki G S A 1960 Measurement of oil-macrlm thickness between disks by electricalconductivity Trans ASME J Basic Engng 82 12

Hamilton G M amp Moore S L 1967 A modimacred gauge for investigating an elastohydrodynamiccontact Proc Inst Mech Engrs 182 251

Hamrock B J 1994 Fundamentals of deguid macrlm lubrication McGraw-Hill

Hosten B 1991 Bulk heterogeneous plane-wave propagation through viscoelastic plates andstratimacred media with large values of frequency-domain Ultrasonics 29 445450

Jacobson B O amp Vinet P 1987 A model for the indeguence of pressure on the bulk modulusand the indeguence of temperature on the solidimacrcation pressure for liquid lubricants Trans

ASME J Tribology 109 709

Johnston G J Wayte R amp Spikes H A 1991 The measurement and study of very thinlubricant macrlms in concentrated contacts Tribol Trans 34 187194

Kinra V K Jaminet P T Zhu C amp Iyer V R 1994 Simultaneous measurement of theacoustical properties of a thin-layered medium the inverse problem J Acoust Soc Am 9530593074

Proc R Soc Lond A (2003)

972 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

0

01

02

03

04

05

07

01 02 03 04 05 06 07

theo

reti

cal

film

thic

knes

s pre

dic

tion (

mm

)

45 kN 112 RPM 60 kN 72 RPM

60 kN 103 RPM 60 kN 128 RPM

60 kN 135 RPM 60 kN 137 RPM

60 kN 178 RPM 60 kN 195 RPM

60 kN 297 RPM 60 kN 375 RPM

75 kN 48 RPM 75 kN 124 RPM

06

measured film thickness (mm)

Figure 14 Comparison of rolling-element-bearing macrlm thickness measured byan ultrasonic means with EHD theoretical solution

water bath machined out of the bearing bush The transducer was spherically focusedand positioned in the water bath so that the wave was focused on the contact betweena ball and the raceway The bearing was loaded hydraulically and rotated by anelectric motor The bearing cavity was regooded with a mineral oil (Shell Turbo T68) Athermocouple was positioned on the outer raceway near the ultrasonic measurementpoint The bearing was loaded to give a contact eclipse between the ball and theouter raceway of semi-major and semi-minor axes 115 and 08 mm respectivelyThe bearing was then rotated and the transducer set to continuously pulse at arepetition rate of 10 kHz

The focal spot size of the transducer was ca 500 mm The maximum rotationalspeed of the bearing in these tests was 375 rpm At this rotational speed theregion of focused ultrasound would remain completely within the lubricated con-tact for ca 05 ms This allowed approximately shyve discrete pulses of ultrasound tobe reregected from the lubricant shylm as each ball passed through the measurementzone Initially a reference reregected pulse was recorded when the bearing was station-ary and there was no ball located over the measurement zone (although the cavitywas still shylled with oil) If a pulse is incident on an EHD shylm its amplitude is reducedbecause part of the wave has been transmitted through the oil shylm into the ball Bycontinuously monitoring the signals reregected from the raceway measurements of theball-raceway contacts were made Of the shyve pulses reregected from the ball-racewaycontact the lowest amplitude pulse was selected for analysis This pulse correspondsto the thinnest measured shylm thickness It should be noted that the resolution of thefocused transducer and the measurement interval are such that it was not possibleto record the horseshoe-shaped minimum shylm-thickness constriction at the contactexit The selected pulse was analysed shyrstly using (53) to calculate the reregection

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 973

film

thic

knes

s (m

m)

1000

100

10

1

01

001

00010 10 20 30 40 50 60

f (MHz)

time of flight limit

resonance method limit

spring model upper limit (R = 09)

spring model lower limit (R = 01)

Figure 15 Limits of operation for macrlm-thickness measurement by ultrasonic means

coemacrcient and then using the spring model to predict the shylm thickness The speedof sound in the oil in the contact is set to c = 4400 m siexcl1 (determined using themethod described in x 3)

Figure 14 shows the measured shylm thickness plotted against a prediction of theshylm thickness from the solution for an elliptical contact of Dowson amp Higginson(1966) (equation (61)) The bearing and lubricant heats up during operation Thetemperature of the entrained oil was monitored and used to determine an appropriateviscosity with which to calculate the shylm thickness in (61) This was why the resultswere not plotted as shylm thickness against speed (as in shygure 11) because viscositywas varying throughout the test

The results in shygure 14 show good agreement between measured lubricant-shylmthickness and that predicted by the EHD regression equations The spread along thex-axis shows the variation in shylm for nominally the same bearing operating conditions(load speed and oil temperature) At this stage it is not clear whether this scatteris a result of the measurement process or whether this is the actual shylm thicknessin the bearing It is worth noting that this measurement process could be improvedif the exact position of the ball could be related to the ultrasonic measurement soallowing a more precise measurement of the minimum shylm thickness

7 Discussion limits of operation

It is instructive to consider the limits of shylm-thickness measurement for a given ultra-sonic frequency The simplest method for determining the thickness of a lubricantlayer providing it is sumacrciently thick is by measuring the ToF through the layerA reregection occurs at the layer front face and another at the back face The thick-ness is readily obtained from the time between the arrival of these pulses multipliedby the acoustic velocity For the method to work the two reregected pulses must besumacrciently discrete and so the propagation distance must be greater than the pulse

Proc R Soc Lond A (2003)

974 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

width and so the minimum shylm thickness detectable by this method is given by

h gtnc

2f (71)

where n is the number of wavelengths in the ultrasonic pulse typically around threeThis measurement limit is plotted in shygure 15 as the minimum frequency requiredto measure a given shylm thickness Conventional ultrasonic non-destructive testingis generally restricted by losses in the propagating media (steel in this case) tofrequencies below 4060 MHz From (71) this means that the ToF method is onlypractically useful for layers of thickness greater than 40 mm This is thicker than thatfound on most commercial bearing systems

A lubricant layer resonates at a frequency given by (23) This equation also givesthe low thickness limit for this technique as the upper frequency output by a giventransducer determined the lowest measurable layer thickness This limit is also shownin shygure 15 for the shyrst through-thickness mode (ie m = 1) So using the highestpractical frequencies shylms greater than 10 mm are measurable by the shylm-resonancemethod

The upper limit of shylm thickness measurable using the spring-model approach isreached as R tends to unity in (27) Experience shows that measurements of R lessthan 09 yield satisfactory results The lowest shylm thickness measurable will dependon the smallest possible value of R This in turn will depend on the signal-to-noiseratio A signal-to-noise ratio of 60 dB is typical for conventional ultrasonic non-destructive testing systems The noise amplitude is thus 1

1000of the pulse amplitude

In the case of a measurement on a real bearing the achievable signal-to-noise ratiowill be reduced by the transducer-bearing reregection coemacrcient and by the attenuationin the bearing shell This means that the pulse incident in the reguid shylm will bereduced from that output by the transducer by a factor of shyve (as a conservativeestimate) Further it is assumed that for reliable measurements a pulse reregectedfrom the oil layer should have an amplitude approximately 20 times that of the noiselevel This results in a minimum measurable reregection coemacrcient of R = 01 Therelationships between the shylm thickness and the transducer frequency for the upperlimit when R = 09 and the lower where R = 01 are shown in shygure 15

This indicates that for a measuring frequency of 60 MHz a lubricant shylm of 2 nmis measurable This opens up the possibility of measuring boundary-type lubricantshylms between machine elements However the models presented here are designedfor a parallel-sided oil layer completely separating the smooth bearing surface If atthese low shylm thickness metal-to-metal contact occurs then transmission will occurat this location In this case some alternative method for interpreting reregectioncoemacrcients will be needed

8 Conclusions

Ultrasound is reregected from the lubricant shylm between bearing surfaces It is possibleto deduce the thickness of the lubricant shylm by comparing the frequency spectrumof the reregected pulse with that of the incident pulse The response of the lubricantlayer to an ultrasonic pulse has been modelled using both a spring-model methodand a continuum method The spring model is suitable for thin lubricant shylms inwhich the wavelength of the ultrasound is much larger than the layer thickness The

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 975

continuum model is valid for all layer thicknesses and allows the prediction of thethrough-thickness resonant frequencies of the lubricant layers Measurement of thesethrough-thickness resonances also provides a means of measuring the layer thickness

Experiments on reguid layers between regat plates and eccentric rings have demon-strated that ultrasound can suitably measure a wide range of liquid layer thicknessThe EHD lubricant shylm that forms between a ball sliding on a regat surface hasalso been measured ultrasonically The measured results agree well with theoreti-cal predictions taking into account the greatly increased speed of sound throughthe lubricant when it is under high pressure Films in the range 50500 nm wererecorded

The approach can also be used to measure shylm thickness in a rolling-elementbearing An ultrasonic transducer was mounted on the bearing raceway and thepulse reregected from the lubricant layer generated as the ball passes was recordedAgain measured results agreed well with theoretical predictions

The lower limit of measurement by this method depends on the signal-to-noiseratio A continuum model showed that using frequencies up to 60 MHz permits themeasurement of 2 nm thick shylms There is no upper limit to shylm-thickness measure-ment Thick shylms (greater than 40 mm) can be measured by a time-of-regight methodFilms of intermediate thickness can be determined by measuring the frequency atwhich the shylm resonates

This work was funded by a grant from the UK Engineering and Physical Sciences ResearchCouncil under the ROPA programme The authors acknowledge the help of Phil Harper of theUniversity of Sheplusmneld for his assistance with some of the measurements

References

Astridge D G amp Longmacreld M D 1967 Capacitance measurement and oil macrlm thickness in alarge radius disc and ring machine Proc Inst Mech Engrs 182 8996

Cameron A amp Gohar R 1966 Theoretical and experimental studies of the oil macrlm in lubricatedpoint contact Proc R Soc Lond A 291 520536

Dowson D amp Higginson G R 1966 Elastohydrodynamic lubrication|the fundamentals of roller

and gear lubrication Oxford Pergamon

Drinkwater B W Dwyer-Joyce R S amp Cawley P 1996 A study of the interaction betweenultrasound and a partially contacting solidsolid interface Proc R Soc Lond A 452 26132628

El-Sisi S I amp Shawki G S A 1960 Measurement of oil-macrlm thickness between disks by electricalconductivity Trans ASME J Basic Engng 82 12

Hamilton G M amp Moore S L 1967 A modimacred gauge for investigating an elastohydrodynamiccontact Proc Inst Mech Engrs 182 251

Hamrock B J 1994 Fundamentals of deguid macrlm lubrication McGraw-Hill

Hosten B 1991 Bulk heterogeneous plane-wave propagation through viscoelastic plates andstratimacred media with large values of frequency-domain Ultrasonics 29 445450

Jacobson B O amp Vinet P 1987 A model for the indeguence of pressure on the bulk modulusand the indeguence of temperature on the solidimacrcation pressure for liquid lubricants Trans

ASME J Tribology 109 709

Johnston G J Wayte R amp Spikes H A 1991 The measurement and study of very thinlubricant macrlms in concentrated contacts Tribol Trans 34 187194

Kinra V K Jaminet P T Zhu C amp Iyer V R 1994 Simultaneous measurement of theacoustical properties of a thin-layered medium the inverse problem J Acoust Soc Am 9530593074

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 973

film

thic

knes

s (m

m)

1000

100

10

1

01

001

00010 10 20 30 40 50 60

f (MHz)

time of flight limit

resonance method limit

spring model upper limit (R = 09)

spring model lower limit (R = 01)

Figure 15 Limits of operation for macrlm-thickness measurement by ultrasonic means

coemacrcient and then using the spring model to predict the shylm thickness The speedof sound in the oil in the contact is set to c = 4400 m siexcl1 (determined using themethod described in x 3)

Figure 14 shows the measured shylm thickness plotted against a prediction of theshylm thickness from the solution for an elliptical contact of Dowson amp Higginson(1966) (equation (61)) The bearing and lubricant heats up during operation Thetemperature of the entrained oil was monitored and used to determine an appropriateviscosity with which to calculate the shylm thickness in (61) This was why the resultswere not plotted as shylm thickness against speed (as in shygure 11) because viscositywas varying throughout the test

The results in shygure 14 show good agreement between measured lubricant-shylmthickness and that predicted by the EHD regression equations The spread along thex-axis shows the variation in shylm for nominally the same bearing operating conditions(load speed and oil temperature) At this stage it is not clear whether this scatteris a result of the measurement process or whether this is the actual shylm thicknessin the bearing It is worth noting that this measurement process could be improvedif the exact position of the ball could be related to the ultrasonic measurement soallowing a more precise measurement of the minimum shylm thickness

7 Discussion limits of operation

It is instructive to consider the limits of shylm-thickness measurement for a given ultra-sonic frequency The simplest method for determining the thickness of a lubricantlayer providing it is sumacrciently thick is by measuring the ToF through the layerA reregection occurs at the layer front face and another at the back face The thick-ness is readily obtained from the time between the arrival of these pulses multipliedby the acoustic velocity For the method to work the two reregected pulses must besumacrciently discrete and so the propagation distance must be greater than the pulse

Proc R Soc Lond A (2003)

974 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

width and so the minimum shylm thickness detectable by this method is given by

h gtnc

2f (71)

where n is the number of wavelengths in the ultrasonic pulse typically around threeThis measurement limit is plotted in shygure 15 as the minimum frequency requiredto measure a given shylm thickness Conventional ultrasonic non-destructive testingis generally restricted by losses in the propagating media (steel in this case) tofrequencies below 4060 MHz From (71) this means that the ToF method is onlypractically useful for layers of thickness greater than 40 mm This is thicker than thatfound on most commercial bearing systems

A lubricant layer resonates at a frequency given by (23) This equation also givesthe low thickness limit for this technique as the upper frequency output by a giventransducer determined the lowest measurable layer thickness This limit is also shownin shygure 15 for the shyrst through-thickness mode (ie m = 1) So using the highestpractical frequencies shylms greater than 10 mm are measurable by the shylm-resonancemethod

The upper limit of shylm thickness measurable using the spring-model approach isreached as R tends to unity in (27) Experience shows that measurements of R lessthan 09 yield satisfactory results The lowest shylm thickness measurable will dependon the smallest possible value of R This in turn will depend on the signal-to-noiseratio A signal-to-noise ratio of 60 dB is typical for conventional ultrasonic non-destructive testing systems The noise amplitude is thus 1

1000of the pulse amplitude

In the case of a measurement on a real bearing the achievable signal-to-noise ratiowill be reduced by the transducer-bearing reregection coemacrcient and by the attenuationin the bearing shell This means that the pulse incident in the reguid shylm will bereduced from that output by the transducer by a factor of shyve (as a conservativeestimate) Further it is assumed that for reliable measurements a pulse reregectedfrom the oil layer should have an amplitude approximately 20 times that of the noiselevel This results in a minimum measurable reregection coemacrcient of R = 01 Therelationships between the shylm thickness and the transducer frequency for the upperlimit when R = 09 and the lower where R = 01 are shown in shygure 15

This indicates that for a measuring frequency of 60 MHz a lubricant shylm of 2 nmis measurable This opens up the possibility of measuring boundary-type lubricantshylms between machine elements However the models presented here are designedfor a parallel-sided oil layer completely separating the smooth bearing surface If atthese low shylm thickness metal-to-metal contact occurs then transmission will occurat this location In this case some alternative method for interpreting reregectioncoemacrcients will be needed

8 Conclusions

Ultrasound is reregected from the lubricant shylm between bearing surfaces It is possibleto deduce the thickness of the lubricant shylm by comparing the frequency spectrumof the reregected pulse with that of the incident pulse The response of the lubricantlayer to an ultrasonic pulse has been modelled using both a spring-model methodand a continuum method The spring model is suitable for thin lubricant shylms inwhich the wavelength of the ultrasound is much larger than the layer thickness The

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 975

continuum model is valid for all layer thicknesses and allows the prediction of thethrough-thickness resonant frequencies of the lubricant layers Measurement of thesethrough-thickness resonances also provides a means of measuring the layer thickness

Experiments on reguid layers between regat plates and eccentric rings have demon-strated that ultrasound can suitably measure a wide range of liquid layer thicknessThe EHD lubricant shylm that forms between a ball sliding on a regat surface hasalso been measured ultrasonically The measured results agree well with theoreti-cal predictions taking into account the greatly increased speed of sound throughthe lubricant when it is under high pressure Films in the range 50500 nm wererecorded

The approach can also be used to measure shylm thickness in a rolling-elementbearing An ultrasonic transducer was mounted on the bearing raceway and thepulse reregected from the lubricant layer generated as the ball passes was recordedAgain measured results agreed well with theoretical predictions

The lower limit of measurement by this method depends on the signal-to-noiseratio A continuum model showed that using frequencies up to 60 MHz permits themeasurement of 2 nm thick shylms There is no upper limit to shylm-thickness measure-ment Thick shylms (greater than 40 mm) can be measured by a time-of-regight methodFilms of intermediate thickness can be determined by measuring the frequency atwhich the shylm resonates

This work was funded by a grant from the UK Engineering and Physical Sciences ResearchCouncil under the ROPA programme The authors acknowledge the help of Phil Harper of theUniversity of Sheplusmneld for his assistance with some of the measurements

References

Astridge D G amp Longmacreld M D 1967 Capacitance measurement and oil macrlm thickness in alarge radius disc and ring machine Proc Inst Mech Engrs 182 8996

Cameron A amp Gohar R 1966 Theoretical and experimental studies of the oil macrlm in lubricatedpoint contact Proc R Soc Lond A 291 520536

Dowson D amp Higginson G R 1966 Elastohydrodynamic lubrication|the fundamentals of roller

and gear lubrication Oxford Pergamon

Drinkwater B W Dwyer-Joyce R S amp Cawley P 1996 A study of the interaction betweenultrasound and a partially contacting solidsolid interface Proc R Soc Lond A 452 26132628

El-Sisi S I amp Shawki G S A 1960 Measurement of oil-macrlm thickness between disks by electricalconductivity Trans ASME J Basic Engng 82 12

Hamilton G M amp Moore S L 1967 A modimacred gauge for investigating an elastohydrodynamiccontact Proc Inst Mech Engrs 182 251

Hamrock B J 1994 Fundamentals of deguid macrlm lubrication McGraw-Hill

Hosten B 1991 Bulk heterogeneous plane-wave propagation through viscoelastic plates andstratimacred media with large values of frequency-domain Ultrasonics 29 445450

Jacobson B O amp Vinet P 1987 A model for the indeguence of pressure on the bulk modulusand the indeguence of temperature on the solidimacrcation pressure for liquid lubricants Trans

ASME J Tribology 109 709

Johnston G J Wayte R amp Spikes H A 1991 The measurement and study of very thinlubricant macrlms in concentrated contacts Tribol Trans 34 187194

Kinra V K Jaminet P T Zhu C amp Iyer V R 1994 Simultaneous measurement of theacoustical properties of a thin-layered medium the inverse problem J Acoust Soc Am 9530593074

Proc R Soc Lond A (2003)

974 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

width and so the minimum shylm thickness detectable by this method is given by

h gtnc

2f (71)

where n is the number of wavelengths in the ultrasonic pulse typically around threeThis measurement limit is plotted in shygure 15 as the minimum frequency requiredto measure a given shylm thickness Conventional ultrasonic non-destructive testingis generally restricted by losses in the propagating media (steel in this case) tofrequencies below 4060 MHz From (71) this means that the ToF method is onlypractically useful for layers of thickness greater than 40 mm This is thicker than thatfound on most commercial bearing systems

A lubricant layer resonates at a frequency given by (23) This equation also givesthe low thickness limit for this technique as the upper frequency output by a giventransducer determined the lowest measurable layer thickness This limit is also shownin shygure 15 for the shyrst through-thickness mode (ie m = 1) So using the highestpractical frequencies shylms greater than 10 mm are measurable by the shylm-resonancemethod

The upper limit of shylm thickness measurable using the spring-model approach isreached as R tends to unity in (27) Experience shows that measurements of R lessthan 09 yield satisfactory results The lowest shylm thickness measurable will dependon the smallest possible value of R This in turn will depend on the signal-to-noiseratio A signal-to-noise ratio of 60 dB is typical for conventional ultrasonic non-destructive testing systems The noise amplitude is thus 1

1000of the pulse amplitude

In the case of a measurement on a real bearing the achievable signal-to-noise ratiowill be reduced by the transducer-bearing reregection coemacrcient and by the attenuationin the bearing shell This means that the pulse incident in the reguid shylm will bereduced from that output by the transducer by a factor of shyve (as a conservativeestimate) Further it is assumed that for reliable measurements a pulse reregectedfrom the oil layer should have an amplitude approximately 20 times that of the noiselevel This results in a minimum measurable reregection coemacrcient of R = 01 Therelationships between the shylm thickness and the transducer frequency for the upperlimit when R = 09 and the lower where R = 01 are shown in shygure 15

This indicates that for a measuring frequency of 60 MHz a lubricant shylm of 2 nmis measurable This opens up the possibility of measuring boundary-type lubricantshylms between machine elements However the models presented here are designedfor a parallel-sided oil layer completely separating the smooth bearing surface If atthese low shylm thickness metal-to-metal contact occurs then transmission will occurat this location In this case some alternative method for interpreting reregectioncoemacrcients will be needed

8 Conclusions

Ultrasound is reregected from the lubricant shylm between bearing surfaces It is possibleto deduce the thickness of the lubricant shylm by comparing the frequency spectrumof the reregected pulse with that of the incident pulse The response of the lubricantlayer to an ultrasonic pulse has been modelled using both a spring-model methodand a continuum method The spring model is suitable for thin lubricant shylms inwhich the wavelength of the ultrasound is much larger than the layer thickness The

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 975

continuum model is valid for all layer thicknesses and allows the prediction of thethrough-thickness resonant frequencies of the lubricant layers Measurement of thesethrough-thickness resonances also provides a means of measuring the layer thickness

Experiments on reguid layers between regat plates and eccentric rings have demon-strated that ultrasound can suitably measure a wide range of liquid layer thicknessThe EHD lubricant shylm that forms between a ball sliding on a regat surface hasalso been measured ultrasonically The measured results agree well with theoreti-cal predictions taking into account the greatly increased speed of sound throughthe lubricant when it is under high pressure Films in the range 50500 nm wererecorded

The approach can also be used to measure shylm thickness in a rolling-elementbearing An ultrasonic transducer was mounted on the bearing raceway and thepulse reregected from the lubricant layer generated as the ball passes was recordedAgain measured results agreed well with theoretical predictions

The lower limit of measurement by this method depends on the signal-to-noiseratio A continuum model showed that using frequencies up to 60 MHz permits themeasurement of 2 nm thick shylms There is no upper limit to shylm-thickness measure-ment Thick shylms (greater than 40 mm) can be measured by a time-of-regight methodFilms of intermediate thickness can be determined by measuring the frequency atwhich the shylm resonates

This work was funded by a grant from the UK Engineering and Physical Sciences ResearchCouncil under the ROPA programme The authors acknowledge the help of Phil Harper of theUniversity of Sheplusmneld for his assistance with some of the measurements

References

Astridge D G amp Longmacreld M D 1967 Capacitance measurement and oil macrlm thickness in alarge radius disc and ring machine Proc Inst Mech Engrs 182 8996

Cameron A amp Gohar R 1966 Theoretical and experimental studies of the oil macrlm in lubricatedpoint contact Proc R Soc Lond A 291 520536

Dowson D amp Higginson G R 1966 Elastohydrodynamic lubrication|the fundamentals of roller

and gear lubrication Oxford Pergamon

Drinkwater B W Dwyer-Joyce R S amp Cawley P 1996 A study of the interaction betweenultrasound and a partially contacting solidsolid interface Proc R Soc Lond A 452 26132628

El-Sisi S I amp Shawki G S A 1960 Measurement of oil-macrlm thickness between disks by electricalconductivity Trans ASME J Basic Engng 82 12

Hamilton G M amp Moore S L 1967 A modimacred gauge for investigating an elastohydrodynamiccontact Proc Inst Mech Engrs 182 251

Hamrock B J 1994 Fundamentals of deguid macrlm lubrication McGraw-Hill

Hosten B 1991 Bulk heterogeneous plane-wave propagation through viscoelastic plates andstratimacred media with large values of frequency-domain Ultrasonics 29 445450

Jacobson B O amp Vinet P 1987 A model for the indeguence of pressure on the bulk modulusand the indeguence of temperature on the solidimacrcation pressure for liquid lubricants Trans

ASME J Tribology 109 709

Johnston G J Wayte R amp Spikes H A 1991 The measurement and study of very thinlubricant macrlms in concentrated contacts Tribol Trans 34 187194

Kinra V K Jaminet P T Zhu C amp Iyer V R 1994 Simultaneous measurement of theacoustical properties of a thin-layered medium the inverse problem J Acoust Soc Am 9530593074

Proc R Soc Lond A (2003)

The measurement of lubricant-macrlm thickness using ultrasound 975

continuum model is valid for all layer thicknesses and allows the prediction of thethrough-thickness resonant frequencies of the lubricant layers Measurement of thesethrough-thickness resonances also provides a means of measuring the layer thickness

Experiments on reguid layers between regat plates and eccentric rings have demon-strated that ultrasound can suitably measure a wide range of liquid layer thicknessThe EHD lubricant shylm that forms between a ball sliding on a regat surface hasalso been measured ultrasonically The measured results agree well with theoreti-cal predictions taking into account the greatly increased speed of sound throughthe lubricant when it is under high pressure Films in the range 50500 nm wererecorded

The approach can also be used to measure shylm thickness in a rolling-elementbearing An ultrasonic transducer was mounted on the bearing raceway and thepulse reregected from the lubricant layer generated as the ball passes was recordedAgain measured results agreed well with theoretical predictions

The lower limit of measurement by this method depends on the signal-to-noiseratio A continuum model showed that using frequencies up to 60 MHz permits themeasurement of 2 nm thick shylms There is no upper limit to shylm-thickness measure-ment Thick shylms (greater than 40 mm) can be measured by a time-of-regight methodFilms of intermediate thickness can be determined by measuring the frequency atwhich the shylm resonates

This work was funded by a grant from the UK Engineering and Physical Sciences ResearchCouncil under the ROPA programme The authors acknowledge the help of Phil Harper of theUniversity of Sheplusmneld for his assistance with some of the measurements

References

Astridge D G amp Longmacreld M D 1967 Capacitance measurement and oil macrlm thickness in alarge radius disc and ring machine Proc Inst Mech Engrs 182 8996

Cameron A amp Gohar R 1966 Theoretical and experimental studies of the oil macrlm in lubricatedpoint contact Proc R Soc Lond A 291 520536

Dowson D amp Higginson G R 1966 Elastohydrodynamic lubrication|the fundamentals of roller

and gear lubrication Oxford Pergamon

Drinkwater B W Dwyer-Joyce R S amp Cawley P 1996 A study of the interaction betweenultrasound and a partially contacting solidsolid interface Proc R Soc Lond A 452 26132628

El-Sisi S I amp Shawki G S A 1960 Measurement of oil-macrlm thickness between disks by electricalconductivity Trans ASME J Basic Engng 82 12

Hamilton G M amp Moore S L 1967 A modimacred gauge for investigating an elastohydrodynamiccontact Proc Inst Mech Engrs 182 251

Hamrock B J 1994 Fundamentals of deguid macrlm lubrication McGraw-Hill

Hosten B 1991 Bulk heterogeneous plane-wave propagation through viscoelastic plates andstratimacred media with large values of frequency-domain Ultrasonics 29 445450

Jacobson B O amp Vinet P 1987 A model for the indeguence of pressure on the bulk modulusand the indeguence of temperature on the solidimacrcation pressure for liquid lubricants Trans

ASME J Tribology 109 709

Johnston G J Wayte R amp Spikes H A 1991 The measurement and study of very thinlubricant macrlms in concentrated contacts Tribol Trans 34 187194

Kinra V K Jaminet P T Zhu C amp Iyer V R 1994 Simultaneous measurement of theacoustical properties of a thin-layered medium the inverse problem J Acoust Soc Am 9530593074

Proc R Soc Lond A (2003)

976 R S Dwyer-Joyce B W Drinkwater and C J Donohoe

Pialucha T amp Cawley P 1994 The detection of thin embedded layers using normal incidenceultrasound Ultrasonics 32 431440

Pialucha T Guyott C C H amp Cawley P 1989 Amplitude spectrum method for the measure-ment of phase velocity Ultrasonics 27 270279

Povey M J W 1997 Ultrasonic techniques for deguids characterisation Academic

Richardson D A amp Borman G L 1991 Using macrbre optics and laser deguorescence for measuringthin oil macrlms with applications to engines SAE Paper 912388

Silk M G 1984 Ultrasonic transducers for nondestructive testing Bristol Hilger

Tattersall H G 1973 The ultrasonic pulse-echo technique as applied to adhesion testing J

Appl Phys 6 819832

Tsukahara Y Nakaso N Kushibiki J-I amp Chubachi N 1989 An acoustic micrometer andits application to layer thickness measurement IEEE Trans UFFC 36 326

Proc R Soc Lond A (2003)